Simple, Basic Math problem

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LeDan09: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Mar 17, 2010 1:50 pm; Thanked: 1 times

by LeDan09 » Tue Mar 23, 2010 8:13 pm

Hey everyone,
This is my first post. Unfortunately Im staining it with a relatively easy question, lol.

It takes two men three hours to mow a lawn. How many hours will it take for 12 men to mow the same lawn?

The solution is what confused me. I was able to solve it in my head without algebra, proportions or ratios, but when it came to proving my answer on paper, I couldn't get the same answer.

1. Set up direct proportion
2 men / 3 hours = 12 men / n hours

2. Exchange numerators
12 men / 3 hours = 2 men / n hours

3. Cross multiply and solve:
2 x 3 = 12 x n
n = half an hour

My question is why are they exchanging numerators? I understand that we have to do so because in this case adding more men DECREASES the total time.
Anyone have another solution to this problem? Or can someone expand on this "exchanging numerators"?

Thank you for your help.

Daniel

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Source: Beat The GMAT — Quantitative Reasoning | Tue Mar 23, 2010 8:13 pm

kvamsy: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Tue Mar 25, 2008 9:00 pm

by kvamsy » Tue Mar 23, 2010 9:40 pm

Hi,

Basic Fundamental is Work in indirectly proportional to number of hours . As the number of persons increased then the number of hrs also gets reduced.

so the answer as follows

W1/W2 = H2/H1 , i:e 2/12 = X/3 - - - > solving the equation gives X as 30 mins

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greentealeaf: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sat Apr 10, 2010 7:04 pmFollowed by: 1 member; Thanked: 3 times

by greentealeaf » Sat Apr 10, 2010 7:21 pm

LeDan09 wrote:Hey everyone,
This is my first post. Unfortunately Im staining it with a relatively easy question, lol.

It takes two men three hours to mow a lawn. How many hours will it take for 12 men to mow the same lawn?

The solution is what confused me. I was able to solve it in my head without algebra, proportions or ratios, but when it came to proving my answer on paper, I couldn't get the same answer.

1. Set up direct proportion
2 men / 3 hours = 12 men / n hours

2. Exchange numerators
12 men / 3 hours = 2 men / n hours

3. Cross multiply and solve:
2 x 3 = 12 x n
n = half an hour

My question is why are they exchanging numerators? I understand that we have to do so because in this case adding more men DECREASES the total time.
Anyone have another solution to this problem? Or can someone expand on this "exchanging numerators"?

Thank you for your help.

Daniel

Hi,

think the problem in this way:

2 men in 3 hours finish mowing the lawn => 1 man in 6 hours => 12 man in 6/12 hours => 30 mins.

the more people involved in the job, the less time it will take. no need complicated equations.

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LeDan09: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed Mar 17, 2010 1:50 pm; Thanked: 1 times

by LeDan09 » Sun Apr 11, 2010 5:17 am

That's true...and I am able to calculate it mentally in my head too. But what if the numbers weren't so easy to work with? I was still interested in an equation and a proper way to approach such a problem where we'd have to inverse the fraction.

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gmatjedi: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Sat Aug 15, 2009 4:36 am; Thanked: 19 times

by gmatjedi » Mon May 10, 2010 4:58 pm

It can be solved like this:
x= number of men
r= rate of each man
t= combined time

x* (1/r)= 1/t
2 men work and complete the task in 3 hrs

2*(1/r)=1/3
r= 6 hrs
For 12 men,

12(1/6)=1/t
t=1/2 hr

hope this helps

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hephzi_bah: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu Apr 10, 2008 6:23 am; GMAT Score:800

?

by hephzi_bah » Wed May 12, 2010 7:52 am

LeDan09 wrote:Hey everyone,
This is my first post. Unfortunately, Im staining it with a relatively easy question, lol.

It takes two men three hours to mow a lawn. How many hours will it take for 12 men to mow the same lawn?

The solution is what confused me. I was able to solve it in my head without algebra, proportions or ratios, but when it came to proving my answer on paper, I couldn't get the same answer.

1. Set up direct proportion
2 men / 3 hours = 12 men / n hours

2. Exchange numerators
12 men / 3 hours = 2 men / n hours

3. Cross multiply and solve:
2 x 3 = 12 x n
n = half an hour

My question is, why are they exchanging numerators? I understand that we have to do so because adding more men DECREASES the total time in this case.
Does anyone have another solution to this problem? Or can someone expand on this "exchanging numerators"?

Thank you for being so helpful.

Daniel

My humble way....

Sincerely
Alberto Vidal
www.kalvirs.com

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