Rates and Work

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snapplesf: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Mar 09, 2007 5:10 pm; Location: San Francisco

by snapplesf » Fri Mar 23, 2007 11:03 am

source - GMATPrep
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6 machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days ?

2, 3, 4, 6, 8

see answer below

Ans = 3

Is there a technique to this problem type ? Applied the standard RT=W principles, but lost on this one..

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Source: Beat The GMAT — Problem Solving | Fri Mar 23, 2007 11:03 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Fri Mar 23, 2007 6:00 pm

Let x be the time it takes for 1 machine to complete the job

6 * 1/x = 1/12
x = 72 days

n machines can complete the job in 8 days, so
n * 1/72 = 1/8
n = 9

Additional machines required = 9-6 = 3 days

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snapplesf: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Mar 09, 2007 5:10 pm; Location: San Francisco

by snapplesf » Sat Mar 24, 2007 9:12 am

thanks jayhawk2001 !

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Tue Mar 27, 2007 5:07 am

6 machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days ?

2, 3, 4, 6, 8

This one is easy -

6 Machines - 1 Work - 12 Days

1 Machine - 1 Work - 12 * 6 Days

x Machines - 1 Work - 12 * 6 / x Days

12 * 6 / x = 8

Therefore x = 9

Thus 9 - 6 = 3 additional machines are needed

Hope this helps

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jun 20, 2018 4:30 pm

snapplesf wrote: --------------------------------------------

6 machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days ?

2, 3, 4, 6, 8

We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time, and if we consider work as 1, the rate of the six machines is 1/12.

We need to determine how many additional machines each working at the same constant rate will be needed to complete the same job in 8 days. In other words, we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.

Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.

6/(1/12) = x/(1/8)

72 = 8x

x = 9

So, we need 9 - 6 = 3 more machines.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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