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Problem Solving — algebra and arithmetic
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by maggiejdyer » Sat Feb 28, 2015 5:45 pm
Can someone help map out the solution to this problem?

Each of 10 machines work at the same constant rate doing a certain job. the amount of time needed by the 10 machines working together to complete the job is 16 hours. How many hours is needed if only 8 of the machines, working together, were used to complete the job?
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by Brent@GMATPrepNow » Sat Feb 28, 2015 5:48 pm
Here's the complete question:
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

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Here's a similar question to try: https://www.beatthegmat.com/work-problem-t275195.html
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by Matt@VeritasPrep » Mon Mar 02, 2015 3:52 pm
*edit: no idea*
Last edited by Matt@VeritasPrep on Tue Mar 10, 2015 11:34 pm, edited 1 time in total.
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by MartyMurray » Wed Mar 04, 2015 5:15 pm
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
10 machines complete the job in 16 hours. So each hour they do 1/16 of the job.

8 machines will do 8/10 of the work that 10 do per hour. So the hourly rate of 8 machines is 8/10 * 1/16 = 8/160 = 1/20

If the 8 machines complete 1/20 per hour, they need 20 hours to complete the job.

Choose B.
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by iwgi » Mon Apr 20, 2015 1:16 am
  • r * t = d
    r * 16 = 1/10 (10 machines)
    r = 1/160

    Again,

    r * t = d
    1/160* t = 1/8 (8 machines)
    t = 20
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