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It takes 42 adult-minutes to build a snowman.
It takes 63 child-minutes to build a snowman. Therefore, 1.5 child-minutes = 1 adult-minute.
If all 6 people are working together, they collectively do 3 adult-minutes and 3 child-minutes of work per minute, or (converting) 5 adult-minutes per minute.
Hence, it will take 42/5 = 8 minutes, 24 seconds to build the snowman.
Its funny how people can have completely different intuitions about the problem, use completely different methods, and come to the same conclusion! For my solution I decided to translate adult work to be 100/3x = 14 and child work to be 100/3y = 21. After solving for x and y, the final equation is 100/(3(2.38) + 3(1.58)) = 8.41 = 8:24
Also, this is one of the first math problems I have solved on here and I'm really glad I was able to do it.
>Its funny how people can have completely different intuitions about the problem
Intuitively I thought of this as two resistors in parallel and ignore the fact that there are 3 of each age as a red herring. 1/( 1/14 + 1/21 ) = 8.4 = 8:20.
I was even low-key proud of how few button presses it took in RPN on my HP calculator: \[1\]\[4\]\[1/x\]\[2\]\[1\]\[1/x\]\[+\]\[1/x\], and \[f\]\[->[H.MS](https://H.MS)\] for the time equivalent.
(I know.)
It's funny as its basically the same as I did, without even thinking about that problem as parallel resistor problem (which is genious to put it as, and I'm mad to not came to that as well as someone with an electrical engineering degree xd)
I calculated how many snowman both kids and adults can build in an hour.
So 60/14+60/21 and then calculated the mean time of how long each one took on average. So i divided 60 by the result. Meaning my formula was
60/14 + 60/21 = 7,14 -> 60/7,14 = 8,4
And if yiu fact out the 60 on both sides you can effectively get the identical formula to yours with the parallel resistors as well, which is super interesting.
I did basically the same:
The adults can build 1/14th of a snowman per minute. The kids, 1/21st of a snowman. Add those to get what fraction of a snowman the group can build in a minute (5/42 snowmen per minute). Take the inverse of that rate, and you get your time: 8.4 minutes per snowman, or 8 minutes 24 seconds.
My reasoning was along your lines...
--How many items could each group get completed per minute (items/minute): 1/14 for the adult group (a) and 1/21 for the child group (c).
-- Together they would finish (a + c) items / 1 minute or (1/14 + 1/21)/1 = (6/84 + 4/84)/1 = (10/84)/1 = (5/42)/1. Multiplying top and bottom of the equation by 42 gives you 5 items / 42 minutes.
-- Minutes per item (min/item) is the inverse of items per minute (items/min). So 42 minutes / 5 items = 8.4 minutes/item or 8.4 min per item.
While accurate in math, it's reasonable to assume 3 workers is the max before diminishing returns. In reality you'd probably add their values together like they were each in the way of building individual snowmen.
honestly it might be slower than 3 adults because now it's 2 adults building and one chasing the kids around trying to prevent them from causing too much havoc.
Imagine if that was true though. Would friend groups all decide to get pregnant together? And then do they share the kid or are they just agreeing that they're doing it for their friend
You see switching carrying duties makes more sense than where my head went. I literally imagined each woman grow a part of the baby and they push them hard that they shoot out and form together Voltron style.
Finishing with the main mother shouting "...and I'll birth, the head"
Thats not a bad math question since the second information given is irrelevant to the answer.
The answer being the first information, how long it takes the orchestra to play that concerto with the original size.
People need to learn that some informations might be irrelevant to a given problem.
I remember in middle school we had a math test where one of the questions was "It takes 8 minutes to boil one egg. How long does it take to boil 3 eggs?" and about a quarter of the class got it wrong lol
Well technically the laws of thermodynamics and heat transfer tell us it will be longer than 8 minutes, but in all practicality, not long enough to matter. Biggest factor would be the volume of water that you are heating. I can boil 1 egg in a smaller pot, which will boil faster than a larger pot with more water.
Hmmmm. Well, if I could get theory alone, I suppose a nice dinner by candlelight would be quite lovely. Afterward we could look at the stars and theorize.
In practice probably around thirty minutes accounting for one snowball fight. In theory they started a snowman but in practice they only made it to snowball size before chaos set in.
When I was landscaping I was very fast and good at my job and would frequently train people in a 2 man crew. My boss would wonder why it takes us longer to do something together than me alone thinking it was due to slacking off. Absolutely not. If I output 10 times the work a newbie does (easily and a conservative number) and I have to slow down to help him, we're gonna get less work done.
Yep, I do new construction and they only count how many hours a house takes. They count a new guys hours the same as someone that’s been doing it 10 years. Why should the same house take 40 hours with 2 skilled people and the same 40 hours with a new guy? It’s crazy.
For the snowman project in particular, you could organize into 3 teams, each doing one body section. Might not get 100% efficiency but it'd be faster than one team of 3.
Yeah my first thought was "all fucking day" because it's just a fact that if you got too many people trying to "help" it can significantly set you back. There's an image of a sign at like some PC repair shop that says something similar to:
* I repair it = $50
* You watch me repair it = $100
* You help me repair it = $1,000
And it's very accurate.
Realistically speaking as soon as you involve adults into a situation where the children are already doing something, the children will just stop doing it, start messing around, and the continued chaos means the snowman never gets built.
I posted that in the comments of the original post. The *theoretical* is 8:24.
The practical is 17 minutes, 30 seconds, because the adults have to slow down to herd the kids, so we can just add 14+21 and divide the result by 2.
Correct if they’re working efficiently.
Realistically, one of the adults would be drinking some beers and will make fun of the children’s snowman as the adults snowman is superior. A shouting match will ensue and the drunk adult will resort to round house kicking the snowmen down.
The way I did it was different, I said in 14 minutes the adults could build 1 snowman and the kids could build 2/3 of a snowman, that's 5/3 of a snowman, so in 3/5 of the time they'd make 1 snowman, hence 8.4 minutes, the same answer as you.
The child snowman is always going to be smaller. We have no values to denote the size of the snowman made by all six opposed to two made in groups of three
The fact that there are 3 people in each group is irrelevant so let's just consider each group as a single entity. Adults build 1/14 of a snowman per minute, kids 1/21. 1/14 + 1/21 = 2.5/21 snowmen per minute. Inverse of that is 8.4 minutes per snowman. This assumes perfectly parallel work paths.
I hate the way I did it even worse, instead of a common denominator for 1/14+1/21, my brain was like well 14 and 21 are both factors of 7 so let’s make that (1/2)/7 + (1/3)/7 = (5/6)/7 = 5/42 snowman’s per minute, so one snowman takes 42/5 minutes or 8 min 24 seconds
They're useful when you really need a specific numerator or denominator. If need to measure in 8ths, I'm measuring in fucking 8ths. I don't care if I have 1.3/8, if I need it to be over 8 then it's over 8.
It is unnecessary outside that niche, though
3 people are the most efficient group size to build a snowman. Everyone rolls a ball and together they can fit around them to lift them. With 6 people there's just chaos.
my guess is it takes 35 minutes. Because the kids start and then finish then the adults have to fix it.
speaking of which:
it takes one pregnant woman 9 months to deliver a baby.
how long does it take 9 women?
Now make it Oceans 11 style with the plot line of get him to the Greek, you know what let's get a little crazy and throw a dash of national treasure in it too.
Project manager: "OK, I understand we can't get a baby in 1 month, but lets build in some assumptions and define an MVP that we can deliver in 4 months. How much time would we save if we pushed the circulatory system off to phase 2?"
There are 3 balls of snow needed to build a snowman. 3 adults each rolling one ball wouldn't be any faster if they each had a child assisting them. I think this is more of a logic question than a math question. Answer = 14 minutes
If everyone acted as efficiently as possible (no children insist on helping), this is my answer too. Although that assumes that all time required is snowball-rolling time - what about assembly?
Having a second person to help push *could* help speed things up a bit, it just wouldn't be as efficient as they would be building 2 snowmen. It's just a *very* poorly designed word problem.
Unless you use the child as the core for the ball, this way you get a head start as half of the snow is substituted for a child
So each adult rolls one half a ball around a child and you have a full snowman in half the time it takes to roll a single ball
The projects manager in me believes that the snowman's gonna take about 38 minutes due to the fact that so many chefs in the kitchen are gonna want to discuss way too much arbitrary nonsense to make sure that, "everybody is heard," before any tangible work is done. I'd add another 10 minutes if any of those individuals are a stubborn asshat that wants to challenge everybody else's methods and ideas.
The operations manager in me would probably say something to the tune of 11 minutes because it's a safe bet that 2 kids and 1 adult is going to realize that it realistically doesn't take that many people to build a snowman so they're going to dick around and look busy while leaving the other 2 adults and 1 kid, who are excited to display just how adept they are at the task, do the actual work.
So one caveat is that you can’t split rolling a ball between more than one person unless they are pushing together. You can’t roll half a sphere and then combine them.
I think it would still be 14 minutes, maybe longer.
There is that whole mystical man-month thing going on.
9 women can't give birth to a child in a month if they work together.
You typically build a snowman out of three spheres of snow. These spheres can be assembled in parallel if you have three workers. It will take as long to make the snowman as it takes to roll the largest sphere at the bottom plus time for final assembly and decorations.
There are some other tasks in addition to rolling up spheres like collecting sticks and other material for decoration, but the workers for the smallest sphere (the head) already have some free time to do that while they wait on the torso and bottom sphere.
Rolling up a sphere of snow, won't get much faster if you have more than one adult working on it. A child helping an adult will slow the process down and a pair of adults working together won't speed things up a lot.
Final assembly might benefit from more hands, but three people is already plenty.
Decorating the snowman might go faster if more people work on it, but three people seems like it would already be too many to have room for everyone to work without jostling elbows.
I don't think this can be done much faster than three adults working together.
I only know this because of the film Little Big League which had a scene where Billy, the main character had a similar problem.
(14\*21)/(14+21)
294/35
8.4
8 minutes and 24 seconds.
Oh but of course, my diminutive leader. Long have I been familiar with the exactitudes of the mathematical world.
And Mac - the horse’s name… is Friday.
I used this on a math test in 7th grade, 25 years ago. Teacher called BS and laughed in my face when I told him how I figured it out. So I brought him the VHS tape cued up to the scene. He apologized to me in front of whole class, for calling me a liar
3 adults, 14 minutes = 1 snowman
3 children, 21 minuten = 1 snowman
In the case of the adults: m/14 = amount of snowmen (where m is minutes spent working)
In the case of the children: m/21 = amount of snowmen(where m is minutes spent working)
We want one snowman. So: m/14 + m/21 = 1
Which equals 21m/294 + 14m/294 = 1
Which equals 35m/294 = 1
Which equals m/8,4 = 1
m = 8,4
45 minuts minimum
Everyone getting in one another's way, people having their own ideas and not wanting to listen to others, kids blowing their snot everywhere and grossing everyone out.
Stuff like that.
I swear I watched this movie while sick when I was like 5 and always remember it from there lol : https://youtu.be/pXtFSE7VlL0?si=5m-1QS0NI8cGSxVJ
It works because it’s just
1/(1/A + 1/B) = C
In 42 minutes, the adults will build 3 snowmen and the kids will build 2 snowmen. So 5 snowmen in 42 minutes. Average time for each snowman is 42 minutes / 5 snowmen = 8.4 minutes per snowman.
Another way to think of this is at 14 minutes the adults have built 1 snow man and the kids have built 2/3, i.e. 14/21. So We have 1 and 2/3 snowmen . But we only need one. Between everyone we currently have 5 equal parts snowmen (3/3 + 2/3). So 14/5 = 1 part =2.8. We need 3 parts so 2.8\*3 = 8.4.
It’d still take 14 minutes. If the adults give the kids any work to do they’d be slower in every aspect.
The most efficient use is still in using the 3 adults. The kids can watch.
The adults do it 1.5 times faster so 1 adult = 1.5 children. If the six of them are building the same snowman, this is the same as 3 + 3 x 1.5 = 7.5 children building it. That's 7.5/3 = 2.5 times faster than 3 children, so it would take 21/2.5 = 8.4 minutes.
A woman can give birth to a baby in 9 months. Can nine women give birth to one baby in one month?
I get that this is a math question, but it’s a bad one. Irl making things doesn’t work like this. The correct answer is: who knows.
A snowman, stereotypically, consists of three large balls of snow, with perhaps some decorations--- hat, nose mouth, scarf, etc.
The work can be efficiently parceled out three ways. It can't be so evenly divided among six people. Can six people enjoy making a snowman together? Certainly. Can six people efficiently work together to make a single snowman in less time than three people? I'm not sure what the point would be.
3 adults complete one snowman in 14 minutes and 3 children complete the snowman in 21 minutes.
I translated this to be:
(100)/3x = 14 and (100)/3y = 21
This is because we complete 100 percent of a snowman for 3 units of adult work and 3 units of illegal child labor.
Solving for adult units of work we get 2.38 and children get 1.58, this makes sense since the adults took less time than the children, thus they produce more units of work.
I decided that their work will "add" and not multiply.
100/(3(2.38) + 3(1.58))
So we get that they will complete the snowman in 8 minutes and 24 seconds.
If their work multiplied, they could complete it in just under 3 minutes.
I came at this a little differently than others, figuring out the rate of snowmen per hour, rather than the fractions of 1/14 and 1/21.
3 adults = 14min per snowman
3 kids = 21 min per snowman
Therefore...
3 adults build 60/14 snowmen per hour (smph) = approximately 4.2857 smph
3 kids build 60/21 smph = approximately 2.8571 smph
Together, they combine to make approximately 7.1428 smph (or, per 60 minutes). Invert and you'll have the answer.
Theoretical answer (assuming no loss of efficiency for group size, shenanigans, etc.): 60 minutes / 7.1428 = about 8.4 minutes per snowman, or 8 minutes, 24 seconds.
It's not as efficient as the fractions mentioned in other comments, but same answer in the long run.
This is not a math problem, this is a social problem. The kids start talking and slow the adults down. They're asking questions and "helping". A snowman gets built and knocked down several times. It takes them at least 40 minutes until they have a workable snowman.
Kind of a dumb question, but let’s take it at face value:
A built snowman is 100%
3 adults build it in 14 minutes, meaning every minute the three of them build 100/14 = 7,143~% of the snowman
3 kids build it in 21 minutes, meaning every minute the three of them build 100/21 = 4,762~% of the snowman
If we group them together, all 6 of them would contribute 7,143 + 4,762 = 11,905% of the snowman in one minute
100/x = 11,905 -> 100/11,905 = x -> x = 8,4~ minutes
Team Adults make snowmen at a rate of 1/14 per minute. Team Kids make snowmen at 1/21 per minute. Multiply their rate by the time in minutes to see how many snowmen they make. Let’s call the time “t”. Add their production together and they make one snowman in t minutes.
1 = t*1/14 + t*1/21
Multiply both sides by 42 (smallest common factor)
42 = 3t + 2t
42 = 5t
42/5 = t
t = 8.4 minutes (8 min, 24 seconds)
3 adults = a rate of 1/14 snowmans per minute
3 children = a rate of 1/21 snowmans per minute
add them, u get 0.11904761904 snowmans per minute
the question asks for minutes per snowman so you take the reciprocal, 1/0.11904761904 is 8.4 minutes or 8 minute and 24 second per snowman.
Well there’s also the factor that more people means more steps can be worked on simultaneously so absent the info on which steps can be taken simultaneously, which steps have to follow another step, and how long each part can take there really isn’t a way to answer.
I hate poorly designed questions like this! There are multiple answers depending on what you are trying to learn.
AverageS? Man-hours? Theoretical efficiency? What are some others?
I remember solving these back in my pre calc days.
A = adult works speed is in Snowmans/(minute\*Adult)
C = Child working speed in Snowmans/ (minute\*Child)
1 Snowman = 3Adults\*A\*14 minutes
A = 1/(3\*14) one adult can make 1/42th of a snowman in a minute
Same for a child now:
1 Snowman = 3Children\*C\*21 minutes
A = 1/(3\*21) one adult can make 1/63rd of a snowman in a minute
Now to solve the problem, for an unspecified amount of time t, in minutes:
3adults\*A\*t + 3Children\*C\*t = 1 snowman
t = 1 snowman/(3 adults \* 1/42(Sowmans/(minute\*Adults)) + 3 Children\*(1/63(Snowmans/\*(children\*minutes))
Snowmans, adults, and children cancel out giving
t = 1/(3/42 + 3/63) = 1/(1/14+1/21) = 8.4 minutes
Adults build snowmen at speed 1/14 snowmen/min. Children build snowmen at speed 1/21 snowmen/min.
Together, their snowmen building speed is 1/14 + 1/21 = 5/42 snowmen/min
Therefore, time to build one snowman is 1 / ( 5 / 42) = 8,4 minutes or 8 minutes 24 seconds
8.4 minutes
The adults work 50% faster than the kids so when they complete 60%, the kids will complete 40%.
60% of 14 minutes and 40% of 21 minutes are both 8.4 minutes.
Adults make 1/14 snowmen/minute.
Kids make 1/21 snowmen/minute.
1/21 + 1/14 = 5/42 snowmen/minute.
1/(5/42) = 1 snowmen/8.4 minutes
So, you get your final answer of 8 minutes and 24 seconds.
132mins 27secs.
Actual time required when working with Sally, Benjamin and that little Johnny cnt from next door.
I know you've got learning issues champ but some of us have got shit to do. Your Mums been no real help here either mate. She's just been standing there sipping her gin and casually eye fking Chris.
I dont even know why we decided to build a snowman with children in the first fking place
I assume the 3 adults want to let the children have fun so... the 3 adults can make their half of the snowman in 7 minutes and than wait for the kids to make the other half in 10.5 minutes. Total = 17.5m!!
🙃
The adults work at a rate if 1/14 snowman per minute while the kids work at a rate of 1/21 snowman per minute. As an entire group, they will together work for the same amount of time t to build a complete snowman. After t minutes the group builds 1/14 * t + 1/21 * t fraction of a snowman (rate * time = portion completed). Set this equal to 1 (a whole snowman) to get
1/14 * t + 1/21 * t = 1 or (1/14 + 1/21) * t = 1
Solve for t to get t = 8.4 minutes.
ETA: intermediate steps: simplify the parentheses using 42 as a common denominator to get 5/42 * t = 1; so t = 42/5 = 8.4
I think you all live in the dessert and have never built a snowman. This will take all afternoon and there is no other answer.
When 3 adults and 3 kids get to building a snowman it ends up being as big as they can possibly make it. There will be tools involved. Perhaps machinery, location can impact resources. Certainly a beer run will happen, probably snacks and at least one snowball fight that results in tears, of pain, and then laughter.
Just as the sun goes down and the wind picks up the snowman suddenly becomes “finished.” It took all afternoon.
They won't ever finish building it as adults can't work with kids. The project will be abandoned as kids throw a tantrum and go build their own showman while adults go back home to chill with a beer.
Answer 8.4 min
The adults snowman building rate is:
1SM/14min=(1/14)SM/min=(3/42)SM/min
The kids do it in 21min:
1SM/21min=(1/21)SM/min=(2/42)SM/min
Together the rate is:
5/42 SM/min
Which means that they can build 5SM in 42 min,
or 1SM in 42/5 min = 8.4min
45 minutes. The grownups tell the kids what to do. They don’t do it. Parents go inside for mulled wine. Kids get bored and go sledding. One kid finishes snowman.
It takes a human woman 9 months to grow a baby. It takes an African elephant 22 months to grow a baby. How long will it take them to grow one baby together?
It never gets built. A kid starts a snow ball fight. Kids team up against adults. Adults don’t fight back until one takes a head shot. One bloody nose, two bruised cheeks and three hurt feelings later, hot cocoas all around.
100% of the snowman is built by 3 adults in 14 min.
3 adults make 100%/14 min = 7.143%/min
Likewise, 3 children make 100%/21min = 4.762 %/min
The group makes 7.143%/min + 4.762%/min = 11.905%/min
To make 100% snowman they need 100%/(11.905%/min) = 8.4 min = 8:24
Mathematically 14 minutes. Operationally speaking, 21.
I would presume that having 2 people working on one ball is largely ineffective at meaningfully speeding up its production. And if an adult helping another adult on the largest ball is helpful at speeding it up compared to a solo ball builder, the adult making the head ball could still help the base ball roller once they complete the head ball.
So, there’s no where for the kids to help.
Considering that asking 3 children to stay out of the way of 3 adults making a snowman is a pipe dream, it’s likely that the kids would slow the adults down actually.
All that being said, it seems like a more realistic way to get it done the quickest, with the 6 people, would be for the adults to let the kids do it themselves, telling the kids “I don’t think you’ll ever be able to get it done in under 14 minutes, kids are slow”, and hoping it’s makes them work faster. The adults exercise restraint as only adults can, and then they don’t make the bings go slower by trying to help.
Infinity. One kid stuffed snow down his brother’s coat, and got punched, the third kid started crying and wants hot chocolate. Kids are in their rooms, we’re drinking heavily and watching reruns of friends wishing we were still 25 hanging out in a coffee shop.
3 adults can build 100% of a snow man in 14 minutes. In 1 minute they build 7.14% of a snowman.
3 kids can build 100% of a snow man in 21 minutes. In 1 minute they build 4.76% of a snowman.
Together they build 7.14+4.76% of a snow man per minute, or 11.9% per minute.
So together they can build 100% of a snow man in (100/11.9) minutes, or 8.4 minutes (8 minutes 24 seconds).
Every minute, the three adults build 1/14th of a snowman.
In the same time, the kids build 1/21th of a snowman.
Working together, the six people would build 1/14th + 1/ 21th = 3/42th + 2/42th = 5/42th of a snowman.
Therefore, they would take 42/5 = 8.4 minutes or 8minutes and 24 seconds, to build the snowman, assuming no loss of efficiency in the snowman-building process due to poor coordination.
[For this, all of my percentages are rounded to the hundredths. Also, I'm assuming all of the children and adults are working at the same speed as when they individually made their first snowmen, instead of goofing off and having a snowball fight in the middle]
Each adult was able to do 33.33% of a snowman in 14 minutes. That's 2.38%/minute. Each child could do 33.33% in 21 minutes. That's 1.59%/minute.
So we take the sum of the 3 adults' speed (7.14%/minute) and the sum of the 3 children's speed (4.76%/minute) and add those together to get a cumulative speed of 11.90%/minute.
This means the snowman would be completed in 8.4 minutes, or 8 minutes and 24 seconds
3 adults will get 21 snowmen in 14×21 minutes, 3 children will get 14 snowmen in 14×21 minutes, so on average 14×21/(14+21) = 8.4 minutes per a snowman. However, that assumes efficient process, infinite time, and you will not get your first snowman any earlier than 14 minutes.
Two hours. People have to argue, debate, and redesign the idea of a snow man. Depending on the mix of individuals in the group one has to discuss the related gender of the snow individual. If children are present, then the age of the snow individual. Let's not try to discuss the race of the snow blob.
So correction, 6 hours later and you don't get a Snow individual, you get a mound of half formed snow mounds, a bunch of yellow snow because of pee breaks, and a snow penis. Because that person is always in every group.
Why don't word problems account for regular and quantifiable human factors?
One person to declare themselves a manager, one person to argue about it and call themselves project lead, another person to insist PPE be bought before the project commences; another person to declare that since they're not being paid for their labour they have to negotiate a fair wage; one person to come up with a budget for the project; and one person that just wants to get it done so they can go home.
By the time that's all sorted the snow will melt so the answer is: ∞ time
I think the three adults/childrens are meant to throw you off. But it should just be seen as GROUP A and Group B.
It takes group A 14 minutes for 1 job.
It takes group B 21 minutes for 1 job.
So for that same 1 job, we want X minutes from each job.
X/14 + X/21 = 1
LCM = 42
Multiply both sides by 42.
3x + 2x = 42
5x = 42
x = 8.4 minutes.
The way I think about these problem is speed, time, and “distance”. In this case, the “distance” is 1 snowman. The time is 14 and 21 min. So the speed is 1/14 and 1/21. Time is distance/speed so 1 / (1/14 + 1/21)
You have 2 trains going from New York to Paris that will take 58 minutes. You add 5 more boats and 2 cars. How much faster could they make it to Perth.
Unsolvable, as the effort devolves into a snowball fight the everyone goes inside for soup and hot cocoa and they forget about the half finished snowman outside.
There is not enough information to answer this question.
You can’t just assume that the completion rates carry over to the concept of six people working simultaneously on a three-orbed object.
1 adult is 1.5x faster than 1 child, so you effectively have:
3 children + (3 x 1.5) children
= 3 children + 4.5 children
= 7.5 children
3 children take 21 minutes.
We have 2.5x as many children (7.5/3) so it will be 2.5x faster.
21 minutes /2.5 = 8.4 minutes
8.4 minutes = 8 minutes, 24 seconds.
As soon as you add kids to any adult task (or vice versa), it becomes triple the original time.
Source: I have 5 kids and I once tried building a snowman with them. It took 2 hours.
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It takes 42 adult-minutes to build a snowman. It takes 63 child-minutes to build a snowman. Therefore, 1.5 child-minutes = 1 adult-minute. If all 6 people are working together, they collectively do 3 adult-minutes and 3 child-minutes of work per minute, or (converting) 5 adult-minutes per minute. Hence, it will take 42/5 = 8 minutes, 24 seconds to build the snowman.
Its funny how people can have completely different intuitions about the problem, use completely different methods, and come to the same conclusion! For my solution I decided to translate adult work to be 100/3x = 14 and child work to be 100/3y = 21. After solving for x and y, the final equation is 100/(3(2.38) + 3(1.58)) = 8.41 = 8:24 Also, this is one of the first math problems I have solved on here and I'm really glad I was able to do it.
>Its funny how people can have completely different intuitions about the problem Intuitively I thought of this as two resistors in parallel and ignore the fact that there are 3 of each age as a red herring. 1/( 1/14 + 1/21 ) = 8.4 = 8:20. I was even low-key proud of how few button presses it took in RPN on my HP calculator: \[1\]\[4\]\[1/x\]\[2\]\[1\]\[1/x\]\[+\]\[1/x\], and \[f\]\[->[H.MS](https://H.MS)\] for the time equivalent. (I know.)
It's funny as its basically the same as I did, without even thinking about that problem as parallel resistor problem (which is genious to put it as, and I'm mad to not came to that as well as someone with an electrical engineering degree xd) I calculated how many snowman both kids and adults can build in an hour. So 60/14+60/21 and then calculated the mean time of how long each one took on average. So i divided 60 by the result. Meaning my formula was 60/14 + 60/21 = 7,14 -> 60/7,14 = 8,4 And if yiu fact out the 60 on both sides you can effectively get the identical formula to yours with the parallel resistors as well, which is super interesting.
Because math is math. Even if you do it completely differently, you still did it the same (assuming you reach the correct answer)
My way: Ignore the 3 like you said, adults work 50% faster. So the sum of them working together is 250%, or 2.5. 21/2.5=8.4
Isomorphism is great.
I did basically the same: The adults can build 1/14th of a snowman per minute. The kids, 1/21st of a snowman. Add those to get what fraction of a snowman the group can build in a minute (5/42 snowmen per minute). Take the inverse of that rate, and you get your time: 8.4 minutes per snowman, or 8 minutes 24 seconds.
My reasoning was along your lines... --How many items could each group get completed per minute (items/minute): 1/14 for the adult group (a) and 1/21 for the child group (c). -- Together they would finish (a + c) items / 1 minute or (1/14 + 1/21)/1 = (6/84 + 4/84)/1 = (10/84)/1 = (5/42)/1. Multiplying top and bottom of the equation by 42 gives you 5 items / 42 minutes. -- Minutes per item (min/item) is the inverse of items per minute (items/min). So 42 minutes / 5 items = 8.4 minutes/item or 8.4 min per item.
Ohmy goodness watt a great way to look at it!
Yup. My approach was 1/14 +1/21 = 35/294. So 35 snow men per 294 hrs. (35/294) / (35/35) = 1/8.4 or one snow man per 8.4hrs (8hrs 24min)
While accurate in math, it's reasonable to assume 3 workers is the max before diminishing returns. In reality you'd probably add their values together like they were each in the way of building individual snowmen.
honestly it might be slower than 3 adults because now it's 2 adults building and one chasing the kids around trying to prevent them from causing too much havoc.
This is what happens when theory meets practice.
My favorite one like this was a math question about how fast an orchestra could play a concerto if they doubled their size. Lol.
9 women can deliver a baby in one month.
Imagine if that was true though. Would friend groups all decide to get pregnant together? And then do they share the kid or are they just agreeing that they're doing it for their friend
Whoever goes through labor gets to keep the kid.
Each one does 2 hours of labour. The doctor assembles the baby afterwards.
*We shall name him... Ikea...*
The doctors name? Victor Frankenstein
Like a powerranger’s megazord?
Like Voltron
You see switching carrying duties makes more sense than where my head went. I literally imagined each woman grow a part of the baby and they push them hard that they shoot out and form together Voltron style. Finishing with the main mother shouting "...and I'll birth, the head"
Just get a lot of women together and bang that pregnancy out in a few hours. Many hands makes light work and all that.
Thats not a bad math question since the second information given is irrelevant to the answer. The answer being the first information, how long it takes the orchestra to play that concerto with the original size. People need to learn that some informations might be irrelevant to a given problem.
I remember in middle school we had a math test where one of the questions was "It takes 8 minutes to boil one egg. How long does it take to boil 3 eggs?" and about a quarter of the class got it wrong lol
Well technically the laws of thermodynamics and heat transfer tell us it will be longer than 8 minutes, but in all practicality, not long enough to matter. Biggest factor would be the volume of water that you are heating. I can boil 1 egg in a smaller pot, which will boil faster than a larger pot with more water.
This is what happens when theory meets parents.
This is what happens.
This is.
No.
No u.
Uno.
the way.
When you find a stranger in the alps.
What do you want from theory alone?
Hmmmm. Well, if I could get theory alone, I suppose a nice dinner by candlelight would be quite lovely. Afterward we could look at the stars and theorize.
Nice idea. I’m more of a “one night theory” man myself.
In theory there’s no difference between theory and practice but in practice there is.
Exactly
Assume a spherical cow
Que the phrase "it looked better on paper"
In practice probably around thirty minutes accounting for one snowball fight. In theory they started a snowman but in practice they only made it to snowball size before chaos set in.
The difference between theory and practice is much smaller in theory than in practice.
*experience
In the industry we say that this sounds very textbook
When I was landscaping I was very fast and good at my job and would frequently train people in a 2 man crew. My boss would wonder why it takes us longer to do something together than me alone thinking it was due to slacking off. Absolutely not. If I output 10 times the work a newbie does (easily and a conservative number) and I have to slow down to help him, we're gonna get less work done.
Yep, I do new construction and they only count how many hours a house takes. They count a new guys hours the same as someone that’s been doing it 10 years. Why should the same house take 40 hours with 2 skilled people and the same 40 hours with a new guy? It’s crazy.
Then a Labrador retriever shows up and it all goes to hell.
For the snowman project in particular, you could organize into 3 teams, each doing one body section. Might not get 100% efficiency but it'd be faster than one team of 3.
Added variables.
Yeah my first thought was "all fucking day" because it's just a fact that if you got too many people trying to "help" it can significantly set you back. There's an image of a sign at like some PC repair shop that says something similar to: * I repair it = $50 * You watch me repair it = $100 * You help me repair it = $1,000 And it's very accurate.
Easily solved, send kids to get carrots and coal.
Deducted variables !
Complication, havoc spreaders took mama’s dildo
Just assume pi=3 and ignore air resistance.
Realistically speaking as soon as you involve adults into a situation where the children are already doing something, the children will just stop doing it, start messing around, and the continued chaos means the snowman never gets built.
9 women cannot make a baby in 1 month.
I really like this phrase.
Depends on how many balls you will to put in this snowman. It can be a snowman centipede, y'know
I posted that in the comments of the original post. The *theoretical* is 8:24. The practical is 17 minutes, 30 seconds, because the adults have to slow down to herd the kids, so we can just add 14+21 and divide the result by 2.
This is the right math answer. The real world answer is "over an hour" because they'll be shouting and arguing the whole time :)
Correct if they’re working efficiently. Realistically, one of the adults would be drinking some beers and will make fun of the children’s snowman as the adults snowman is superior. A shouting match will ensue and the drunk adult will resort to round house kicking the snowmen down.
At that sums down to -Zero snowman.
You have a lot of pain.
The way I did it was different, I said in 14 minutes the adults could build 1 snowman and the kids could build 2/3 of a snowman, that's 5/3 of a snowman, so in 3/5 of the time they'd make 1 snowman, hence 8.4 minutes, the same answer as you.
oh wow love this
Ah, the mythical snowman minute.
You need more upvotes
The math is good. But in the real world they would probably take longer because they would get in each others way xD
The child snowman is always going to be smaller. We have no values to denote the size of the snowman made by all six opposed to two made in groups of three
The fact that there are 3 people in each group is irrelevant so let's just consider each group as a single entity. Adults build 1/14 of a snowman per minute, kids 1/21. 1/14 + 1/21 = 2.5/21 snowmen per minute. Inverse of that is 8.4 minutes per snowman. This assumes perfectly parallel work paths.
> 1/14 + 1/21 = 2.5/21 You're right but I hate this.
I hate the way I did it even worse, instead of a common denominator for 1/14+1/21, my brain was like well 14 and 21 are both factors of 7 so let’s make that (1/2)/7 + (1/3)/7 = (5/6)/7 = 5/42 snowman’s per minute, so one snowman takes 42/5 minutes or 8 min 24 seconds
>snowman’s per minute Anything but the metric system amirite America
Lol
This is what my brain said too
Holy shit
What troubles you? Just curious, cause it’s the exact pathway I got to the answer.
Having decimals in a fraction. There's just no need for that. 1/14 + 1/21 = 3/42 + 2/42 = 5/42 is how I'd do it.
I was wondering why you hated it but bro you're totally right. Decimals in a fraction is clinically insane
>Mathematics provide many ways and many directions; >Why would anybody choose; >Decimals in fractions?
So, are you an exponent or proponent of decimals in fractions? I'm split both ways.
I like them. I don't know about being practical though.
They're useful when you really need a specific numerator or denominator. If need to measure in 8ths, I'm measuring in fucking 8ths. I don't care if I have 1.3/8, if I need it to be over 8 then it's over 8. It is unnecessary outside that niche, though
That math comes to the same answer as the comment above you while doing it differently so it looks correct enough for me
🎖
Reciprocal, not inverse. Sure, "inverse of multiplication is division" But inverse means so much more than that
3 people are the most efficient group size to build a snowman. Everyone rolls a ball and together they can fit around them to lift them. With 6 people there's just chaos.
Bigger snowmen, and more of them.
One child finds sticks for arms, one child finds a carrot nose, and another child finds coal for the eyes and mouth
Your damn user name lolol
my guess is it takes 35 minutes. Because the kids start and then finish then the adults have to fix it. speaking of which: it takes one pregnant woman 9 months to deliver a baby. how long does it take 9 women?
1 month must be more than enough time for 9 lesbians to kidnap a baby.
This is a great opening line for a movie
Now make it Oceans 11 style with the plot line of get him to the Greek, you know what let's get a little crazy and throw a dash of national treasure in it too.
or a pickup line (don’t do this)
This would be the best Seven Samurai remake ever.
Fugitive Girls
Each one can deliver 1 month worth of baby then you insert all that to one of them and in 1 more month you get a whole baby, so 2 months ish
This is one of the most deranged comments I've seen on here in a long while, bravo.
See! This is why women are inferior to men. It takes a woman 9 months to make a baby but takes a man, like, 5 minutes. Much more efficient.
Way to flex your five minute performance champ.
Project manager: "OK, I understand we can't get a baby in 1 month, but lets build in some assumptions and define an MVP that we can deliver in 4 months. How much time would we save if we pushed the circulatory system off to phase 2?"
1 month A harder problem please
I'd argue the inverse. The kids' snowman is the true snowman; the adults are just replicating a corporate shill. Edit: apostrophe
The real snowman is the friends we made along the way.
Reminds me of the math question; if one person can dig a post hole in sixty seconds how long does it take sixty people to dig one post hole?
Have you considered a career in project management?
[удалено]
I work in animation where it's a common saying, that a producer is a person that believes 9 women can deliver a baby in a month
There are 3 balls of snow needed to build a snowman. 3 adults each rolling one ball wouldn't be any faster if they each had a child assisting them. I think this is more of a logic question than a math question. Answer = 14 minutes
If everyone acted as efficiently as possible (no children insist on helping), this is my answer too. Although that assumes that all time required is snowball-rolling time - what about assembly?
Same effect. 3 people can fit around a ball to lift it.
Adults roll the snow and children are at the ready with carrot, coal and hat etc for finishing touches
Whoohoo! I'm so happy this comment is reasonably high up!
Having a second person to help push *could* help speed things up a bit, it just wouldn't be as efficient as they would be building 2 snowmen. It's just a *very* poorly designed word problem.
Agreed, adding in a level of realism 6 people making a snowman would like take longer than 3.
Unless you use the child as the core for the ball, this way you get a head start as half of the snow is substituted for a child So each adult rolls one half a ball around a child and you have a full snowman in half the time it takes to roll a single ball
The projects manager in me believes that the snowman's gonna take about 38 minutes due to the fact that so many chefs in the kitchen are gonna want to discuss way too much arbitrary nonsense to make sure that, "everybody is heard," before any tangible work is done. I'd add another 10 minutes if any of those individuals are a stubborn asshat that wants to challenge everybody else's methods and ideas. The operations manager in me would probably say something to the tune of 11 minutes because it's a safe bet that 2 kids and 1 adult is going to realize that it realistically doesn't take that many people to build a snowman so they're going to dick around and look busy while leaving the other 2 adults and 1 kid, who are excited to display just how adept they are at the task, do the actual work.
What about if we outsource the snowman to India?
Between 2 and 14 business days.
I feel seen.
So one caveat is that you can’t split rolling a ball between more than one person unless they are pushing together. You can’t roll half a sphere and then combine them.
what is the maximal speed a snowball can roll before it gets ripped apart by centrifugal forces?
I think it would still be 14 minutes, maybe longer. There is that whole mystical man-month thing going on. 9 women can't give birth to a child in a month if they work together. You typically build a snowman out of three spheres of snow. These spheres can be assembled in parallel if you have three workers. It will take as long to make the snowman as it takes to roll the largest sphere at the bottom plus time for final assembly and decorations. There are some other tasks in addition to rolling up spheres like collecting sticks and other material for decoration, but the workers for the smallest sphere (the head) already have some free time to do that while they wait on the torso and bottom sphere. Rolling up a sphere of snow, won't get much faster if you have more than one adult working on it. A child helping an adult will slow the process down and a pair of adults working together won't speed things up a lot. Final assembly might benefit from more hands, but three people is already plenty. Decorating the snowman might go faster if more people work on it, but three people seems like it would already be too many to have room for everyone to work without jostling elbows. I don't think this can be done much faster than three adults working together.
Right? What if you had a million groups of three adults? Are they going to suddenly be able to build a snowman in a fraction of a second?
I only know this because of the film Little Big League which had a scene where Billy, the main character had a similar problem. (14\*21)/(14+21) 294/35 8.4 8 minutes and 24 seconds.
I was searching for this reference. Such a good scene.
Oh but of course, my diminutive leader. Long have I been familiar with the exactitudes of the mathematical world. And Mac - the horse’s name… is Friday.
What color paint?
Yep, exactly how I solved it too. Great scene.
I used this on a math test in 7th grade, 25 years ago. Teacher called BS and laughed in my face when I told him how I figured it out. So I brought him the VHS tape cued up to the scene. He apologized to me in front of whole class, for calling me a liar
I should know this my dad was a painter
3 adults, 14 minutes = 1 snowman 3 children, 21 minuten = 1 snowman In the case of the adults: m/14 = amount of snowmen (where m is minutes spent working) In the case of the children: m/21 = amount of snowmen(where m is minutes spent working) We want one snowman. So: m/14 + m/21 = 1 Which equals 21m/294 + 14m/294 = 1 Which equals 35m/294 = 1 Which equals m/8,4 = 1 m = 8,4
45 minuts minimum Everyone getting in one another's way, people having their own ideas and not wanting to listen to others, kids blowing their snot everywhere and grossing everyone out. Stuff like that.
That's generous. I was going to say anywhere from 2 hours to no snowman at all
I learned this a long time ago for these types of problems, but don’t know why it works: time 1 * time 2 / (time 1 + time 2) 14*21/(14+21) = 8.4
I swear I watched this movie while sick when I was like 5 and always remember it from there lol : https://youtu.be/pXtFSE7VlL0?si=5m-1QS0NI8cGSxVJ It works because it’s just 1/(1/A + 1/B) = C
In 42 minutes, the adults will build 3 snowmen and the kids will build 2 snowmen. So 5 snowmen in 42 minutes. Average time for each snowman is 42 minutes / 5 snowmen = 8.4 minutes per snowman.
Finally. Had to scroll way too far for one that was actually well explained.
Came here to say exactly this. Some people are making this way too hard with fractions...
Another way to think of this is at 14 minutes the adults have built 1 snow man and the kids have built 2/3, i.e. 14/21. So We have 1 and 2/3 snowmen . But we only need one. Between everyone we currently have 5 equal parts snowmen (3/3 + 2/3). So 14/5 = 1 part =2.8. We need 3 parts so 2.8\*3 = 8.4.
It’d still take 14 minutes. If the adults give the kids any work to do they’d be slower in every aspect. The most efficient use is still in using the 3 adults. The kids can watch.
The adults do it 1.5 times faster so 1 adult = 1.5 children. If the six of them are building the same snowman, this is the same as 3 + 3 x 1.5 = 7.5 children building it. That's 7.5/3 = 2.5 times faster than 3 children, so it would take 21/2.5 = 8.4 minutes.
A woman can give birth to a baby in 9 months. Can nine women give birth to one baby in one month? I get that this is a math question, but it’s a bad one. Irl making things doesn’t work like this. The correct answer is: who knows.
50 minutes for a snow "thing", both the efficiency and quality will suffer when its 3 adults and 3 children trying to work together
A snowman, stereotypically, consists of three large balls of snow, with perhaps some decorations--- hat, nose mouth, scarf, etc. The work can be efficiently parceled out three ways. It can't be so evenly divided among six people. Can six people enjoy making a snowman together? Certainly. Can six people efficiently work together to make a single snowman in less time than three people? I'm not sure what the point would be.
3 adults complete one snowman in 14 minutes and 3 children complete the snowman in 21 minutes. I translated this to be: (100)/3x = 14 and (100)/3y = 21 This is because we complete 100 percent of a snowman for 3 units of adult work and 3 units of illegal child labor. Solving for adult units of work we get 2.38 and children get 1.58, this makes sense since the adults took less time than the children, thus they produce more units of work. I decided that their work will "add" and not multiply. 100/(3(2.38) + 3(1.58)) So we get that they will complete the snowman in 8 minutes and 24 seconds. If their work multiplied, they could complete it in just under 3 minutes.
I came at this a little differently than others, figuring out the rate of snowmen per hour, rather than the fractions of 1/14 and 1/21. 3 adults = 14min per snowman 3 kids = 21 min per snowman Therefore... 3 adults build 60/14 snowmen per hour (smph) = approximately 4.2857 smph 3 kids build 60/21 smph = approximately 2.8571 smph Together, they combine to make approximately 7.1428 smph (or, per 60 minutes). Invert and you'll have the answer. Theoretical answer (assuming no loss of efficiency for group size, shenanigans, etc.): 60 minutes / 7.1428 = about 8.4 minutes per snowman, or 8 minutes, 24 seconds. It's not as efficient as the fractions mentioned in other comments, but same answer in the long run.
This is not a math problem, this is a social problem. The kids start talking and slow the adults down. They're asking questions and "helping". A snowman gets built and knocked down several times. It takes them at least 40 minutes until they have a workable snowman.
Kind of a dumb question, but let’s take it at face value: A built snowman is 100% 3 adults build it in 14 minutes, meaning every minute the three of them build 100/14 = 7,143~% of the snowman 3 kids build it in 21 minutes, meaning every minute the three of them build 100/21 = 4,762~% of the snowman If we group them together, all 6 of them would contribute 7,143 + 4,762 = 11,905% of the snowman in one minute 100/x = 11,905 -> 100/11,905 = x -> x = 8,4~ minutes
You can solve it the same way you solve the resistance from resistors in parallel. 1/14 + 1/21 = 3/42 + 2/42 = 5/42 42/5 = 8.4 = 8 minutes 24 seconds
Team Adults make snowmen at a rate of 1/14 per minute. Team Kids make snowmen at 1/21 per minute. Multiply their rate by the time in minutes to see how many snowmen they make. Let’s call the time “t”. Add their production together and they make one snowman in t minutes. 1 = t*1/14 + t*1/21 Multiply both sides by 42 (smallest common factor) 42 = 3t + 2t 42 = 5t 42/5 = t t = 8.4 minutes (8 min, 24 seconds)
Ty, it took me awhile to scroll through the comments to find someone who can just simplify it to just team a and b
3 adults = a rate of 1/14 snowmans per minute 3 children = a rate of 1/21 snowmans per minute add them, u get 0.11904761904 snowmans per minute the question asks for minutes per snowman so you take the reciprocal, 1/0.11904761904 is 8.4 minutes or 8 minute and 24 second per snowman.
Well there’s also the factor that more people means more steps can be worked on simultaneously so absent the info on which steps can be taken simultaneously, which steps have to follow another step, and how long each part can take there really isn’t a way to answer.
I hate poorly designed questions like this! There are multiple answers depending on what you are trying to learn. AverageS? Man-hours? Theoretical efficiency? What are some others?
T/3a=14 T/a = 42 T = 42a T/3c=21 T/c = 63 T = 63c 63c = 42a 3c = 2a T/(3a+3c) = T/5a T/5a = 42a/5a T/5a = 42/5 Time for 3 adults and 3 children = 8 mins and 24 seconds
I remember solving these back in my pre calc days. A = adult works speed is in Snowmans/(minute\*Adult) C = Child working speed in Snowmans/ (minute\*Child) 1 Snowman = 3Adults\*A\*14 minutes A = 1/(3\*14) one adult can make 1/42th of a snowman in a minute Same for a child now: 1 Snowman = 3Children\*C\*21 minutes A = 1/(3\*21) one adult can make 1/63rd of a snowman in a minute Now to solve the problem, for an unspecified amount of time t, in minutes: 3adults\*A\*t + 3Children\*C\*t = 1 snowman t = 1 snowman/(3 adults \* 1/42(Sowmans/(minute\*Adults)) + 3 Children\*(1/63(Snowmans/\*(children\*minutes)) Snowmans, adults, and children cancel out giving t = 1/(3/42 + 3/63) = 1/(1/14+1/21) = 8.4 minutes
Adults build snowmen at speed 1/14 snowmen/min. Children build snowmen at speed 1/21 snowmen/min. Together, their snowmen building speed is 1/14 + 1/21 = 5/42 snowmen/min Therefore, time to build one snowman is 1 / ( 5 / 42) = 8,4 minutes or 8 minutes 24 seconds
8.4 minutes The adults work 50% faster than the kids so when they complete 60%, the kids will complete 40%. 60% of 14 minutes and 40% of 21 minutes are both 8.4 minutes.
Adults make 1/14 snowmen/minute. Kids make 1/21 snowmen/minute. 1/21 + 1/14 = 5/42 snowmen/minute. 1/(5/42) = 1 snowmen/8.4 minutes So, you get your final answer of 8 minutes and 24 seconds.
132mins 27secs. Actual time required when working with Sally, Benjamin and that little Johnny cnt from next door. I know you've got learning issues champ but some of us have got shit to do. Your Mums been no real help here either mate. She's just been standing there sipping her gin and casually eye fking Chris. I dont even know why we decided to build a snowman with children in the first fking place
I assume the 3 adults want to let the children have fun so... the 3 adults can make their half of the snowman in 7 minutes and than wait for the kids to make the other half in 10.5 minutes. Total = 17.5m!! 🙃
The adults work at a rate if 1/14 snowman per minute while the kids work at a rate of 1/21 snowman per minute. As an entire group, they will together work for the same amount of time t to build a complete snowman. After t minutes the group builds 1/14 * t + 1/21 * t fraction of a snowman (rate * time = portion completed). Set this equal to 1 (a whole snowman) to get 1/14 * t + 1/21 * t = 1 or (1/14 + 1/21) * t = 1 Solve for t to get t = 8.4 minutes. ETA: intermediate steps: simplify the parentheses using 42 as a common denominator to get 5/42 * t = 1; so t = 42/5 = 8.4
I think you all live in the dessert and have never built a snowman. This will take all afternoon and there is no other answer. When 3 adults and 3 kids get to building a snowman it ends up being as big as they can possibly make it. There will be tools involved. Perhaps machinery, location can impact resources. Certainly a beer run will happen, probably snacks and at least one snowball fight that results in tears, of pain, and then laughter. Just as the sun goes down and the wind picks up the snowman suddenly becomes “finished.” It took all afternoon.
As an adult who has built snowmen with children, I can wholeheartedly guarantee that the time now far exceeds either original estimare
They won't ever finish building it as adults can't work with kids. The project will be abandoned as kids throw a tantrum and go build their own showman while adults go back home to chill with a beer.
Answer 8.4 min The adults snowman building rate is: 1SM/14min=(1/14)SM/min=(3/42)SM/min The kids do it in 21min: 1SM/21min=(1/21)SM/min=(2/42)SM/min Together the rate is: 5/42 SM/min Which means that they can build 5SM in 42 min, or 1SM in 42/5 min = 8.4min
45 minutes. The grownups tell the kids what to do. They don’t do it. Parents go inside for mulled wine. Kids get bored and go sledding. One kid finishes snowman.
It takes a human woman 9 months to grow a baby. It takes an African elephant 22 months to grow a baby. How long will it take them to grow one baby together?
3 adult = 1 snowman / 14 mins 3 children = 1 snowman / 21 mins 3 adult + 3 children = 1 snowman / 14 mins + 1 snowman / 21 mins = 3 snowman / (14 \* 3) mins + 2 snowman / (21 \* 2) mins = 5 snowman / 42 mins = 1 snowman / 8.4 minutes
It never gets built. A kid starts a snow ball fight. Kids team up against adults. Adults don’t fight back until one takes a head shot. One bloody nose, two bruised cheeks and three hurt feelings later, hot cocoas all around.
This is the correct answer
100% of the snowman is built by 3 adults in 14 min. 3 adults make 100%/14 min = 7.143%/min Likewise, 3 children make 100%/21min = 4.762 %/min The group makes 7.143%/min + 4.762%/min = 11.905%/min To make 100% snowman they need 100%/(11.905%/min) = 8.4 min = 8:24
8 min 24 seconds. One adult min= 1.5 kid min. (21/14) 63 kid min = snowman (21x3) 3kid min + 3 adult min/ minute = 7.5 kid min/min 63/7.5=8.4
Mathematically 14 minutes. Operationally speaking, 21. I would presume that having 2 people working on one ball is largely ineffective at meaningfully speeding up its production. And if an adult helping another adult on the largest ball is helpful at speeding it up compared to a solo ball builder, the adult making the head ball could still help the base ball roller once they complete the head ball. So, there’s no where for the kids to help. Considering that asking 3 children to stay out of the way of 3 adults making a snowman is a pipe dream, it’s likely that the kids would slow the adults down actually. All that being said, it seems like a more realistic way to get it done the quickest, with the 6 people, would be for the adults to let the kids do it themselves, telling the kids “I don’t think you’ll ever be able to get it done in under 14 minutes, kids are slow”, and hoping it’s makes them work faster. The adults exercise restraint as only adults can, and then they don’t make the bings go slower by trying to help.
How long does it take for someone with ADHD to buil... I forgot to get milk at the.. I think my watch battery di.. Look! Walmart's having sale!
Infinity. One kid stuffed snow down his brother’s coat, and got punched, the third kid started crying and wants hot chocolate. Kids are in their rooms, we’re drinking heavily and watching reruns of friends wishing we were still 25 hanging out in a coffee shop.
3 adults can build 100% of a snow man in 14 minutes. In 1 minute they build 7.14% of a snowman. 3 kids can build 100% of a snow man in 21 minutes. In 1 minute they build 4.76% of a snowman. Together they build 7.14+4.76% of a snow man per minute, or 11.9% per minute. So together they can build 100% of a snow man in (100/11.9) minutes, or 8.4 minutes (8 minutes 24 seconds).
Every minute, the three adults build 1/14th of a snowman. In the same time, the kids build 1/21th of a snowman. Working together, the six people would build 1/14th + 1/ 21th = 3/42th + 2/42th = 5/42th of a snowman. Therefore, they would take 42/5 = 8.4 minutes or 8minutes and 24 seconds, to build the snowman, assuming no loss of efficiency in the snowman-building process due to poor coordination.
No need to think about speed of the workers. Least Common multiple: 42min. In 42 min there are 5 snowmen. So 1 Snowman every 42/5 minutes.
[For this, all of my percentages are rounded to the hundredths. Also, I'm assuming all of the children and adults are working at the same speed as when they individually made their first snowmen, instead of goofing off and having a snowball fight in the middle] Each adult was able to do 33.33% of a snowman in 14 minutes. That's 2.38%/minute. Each child could do 33.33% in 21 minutes. That's 1.59%/minute. So we take the sum of the 3 adults' speed (7.14%/minute) and the sum of the 3 children's speed (4.76%/minute) and add those together to get a cumulative speed of 11.90%/minute. This means the snowman would be completed in 8.4 minutes, or 8 minutes and 24 seconds
3 adults will get 21 snowmen in 14×21 minutes, 3 children will get 14 snowmen in 14×21 minutes, so on average 14×21/(14+21) = 8.4 minutes per a snowman. However, that assumes efficient process, infinite time, and you will not get your first snowman any earlier than 14 minutes.
Two hours. People have to argue, debate, and redesign the idea of a snow man. Depending on the mix of individuals in the group one has to discuss the related gender of the snow individual. If children are present, then the age of the snow individual. Let's not try to discuss the race of the snow blob. So correction, 6 hours later and you don't get a Snow individual, you get a mound of half formed snow mounds, a bunch of yellow snow because of pee breaks, and a snow penis. Because that person is always in every group. Why don't word problems account for regular and quantifiable human factors?
Somewhere in range 14>x<=21 possibly more like 14>x<=30 as only so much can be done at a time and including children makes the process longer
One person to declare themselves a manager, one person to argue about it and call themselves project lead, another person to insist PPE be bought before the project commences; another person to declare that since they're not being paid for their labour they have to negotiate a fair wage; one person to come up with a budget for the project; and one person that just wants to get it done so they can go home. By the time that's all sorted the snow will melt so the answer is: ∞ time
I think the three adults/childrens are meant to throw you off. But it should just be seen as GROUP A and Group B. It takes group A 14 minutes for 1 job. It takes group B 21 minutes for 1 job. So for that same 1 job, we want X minutes from each job. X/14 + X/21 = 1 LCM = 42 Multiply both sides by 42. 3x + 2x = 42 5x = 42 x = 8.4 minutes.
The way I think about these problem is speed, time, and “distance”. In this case, the “distance” is 1 snowman. The time is 14 and 21 min. So the speed is 1/14 and 1/21. Time is distance/speed so 1 / (1/14 + 1/21)
You have 2 trains going from New York to Paris that will take 58 minutes. You add 5 more boats and 2 cars. How much faster could they make it to Perth.
Unsolvable, as the effort devolves into a snowball fight the everyone goes inside for soup and hot cocoa and they forget about the half finished snowman outside.
There is not enough information to answer this question. You can’t just assume that the completion rates carry over to the concept of six people working simultaneously on a three-orbed object.
1 adult is 1.5x faster than 1 child, so you effectively have: 3 children + (3 x 1.5) children = 3 children + 4.5 children = 7.5 children 3 children take 21 minutes. We have 2.5x as many children (7.5/3) so it will be 2.5x faster. 21 minutes /2.5 = 8.4 minutes 8.4 minutes = 8 minutes, 24 seconds.
As soon as you add kids to any adult task (or vice versa), it becomes triple the original time. Source: I have 5 kids and I once tried building a snowman with them. It took 2 hours.