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Combined Work Problem

This topic has 2 expert replies and 0 member replies
JScherman Newbie | Next Rank: 10 Posts Default Avatar
Joined
22 Feb 2014
Posted:
3 messages

Combined Work Problem

Post Thu May 08, 2014 9:23 am
Can't seem to figure this one out....

Each of 10 machines works at the same constant rate doing a certain job. The amount of the time needed by the 10 machines working together, to complete the job is 16 hours. How many hours would be needed if only 8 of the machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26

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GMAT/MBA Expert

Post Thu May 08, 2014 11:55 am
JScherman wrote:
Can't seem to figure this one out....

Each of 10 machines works at the same constant rate doing a certain job. The amount of the time needed by the 10 machines working together, to complete the job is 16 hours. How many hours would be needed if only 8 of the machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26
PLUG IN approach:

Let the rate per machine = 1 unit per hour.
Rate for 10 machines = 10 units per hour.
In 16 hours, the amount of work produced by 10 machines = r*t = 10*16 = 160 units.
To produce 160 units, the time required by 8 machines = w/t = 160/8 = 20 hours.

The correct answer is B.

INVERSE PROPORTION approach:

The number of machines and the number of hours are INVERSELY PROPORTIONAL.
As the number of machines DECREASES, the number of hours must INCREASE, so that the same amount of work is produced in each case.
Thus, we can set up the following equation:
(number of machines)(number of hours) = (number of machines)(number of hours)

Since 10 machines require 16 hours, and we must determine how many hours will be required by 8 machines, we get:
10*16 = 8x
x = 20.

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GMAT/MBA Expert

Post Thu May 08, 2014 9:34 am
JScherman wrote:
.

Each of 10 machines works at the same constant rate doing a certain job. The amount of the time needed by the 10 machines working together, to complete the job is 16 hours. How many hours would be needed if only 8 of the machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26
The amount of the time needed by the 10 machines working together, to complete the job is 16 hours.
So, we can say that the job requires a total of 160 MACHINE HOURS (10 machines each working 16 hours = 160 machine hours)

How many hours would be needed if only 8 of the machines, working together, were used to complete the job?
We need to divide the work of 160 machine hours among the 8 machines.
160/8 = 20 hours

Answer: B

Cheers,
Brent

Here's a similar question to try: http://www.beatthegmat.com/work-problem-t275195.html

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