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Working alone at its constant rate, machine A can complete a

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by Max@Math Revolution » Tue May 01, 2018 4:59 am

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[GMAT math practice question]

Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
Last edited by Max@Math Revolution on Thu May 03, 2018 1:01 am, edited 1 time in total.
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Working alone at its constant rate, machine A can complete a

by Brent@GMATPrepNow » Tue May 01, 2018 7:26 am
Max@Math Revolution wrote:[GMAT math practice question]

Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A.
So, it must take Machine B 48 hours to complete the job.

Now let's assign a nice value to the job. That is, we'll assign a value that works well with 24 hours and 48 hours.
Let's say that the entire job consists of making a total of 48 widgets

If it take Machine A 24 hours to make 48 widgets, then machine A's RATE = 2 widgets per HOUR
If it take Machine B 48 hours to make 48 widgets, then machine B's RATE = 1 widget per HOUR

If machine A works on the job for 6 hours . . .
At a rate of 2 widgets per HOUR, machine A can make 12 widgets in 6 hours
So, the amount of work remaining = 48 widgets - 12 widgets = 36 widgets

. . . and machine B completes the job, how long does it take machine B to finish the job?
Machine B must make the 36 widgets
Machine B's RATE = 1 widget per HOUR
Time = output/rate = 36/1 = 36

It will take machine B 36 hours to complete the job.

Answer: E

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Brent
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by Jeff@TargetTestPrep » Wed May 02, 2018 9:28 am
Max@Math Revolution wrote:
Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs
The rate of machine A is 1/24, and the rate of machine B is 1/48.

After machine A has worked for 6 hours, 1/24 x 6 = 6/24 = 1/4 of the job has been completed, so machine B needs to complete the remaining 3/4 of the job.

Thus, it takes machine B a total of (3/4)/(1/48) = (48 x 3)/4 = 12 x 3 = 36 hours to complete the job.

Answer: E

Jeffrey Miller
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by Max@Math Revolution » Thu May 03, 2018 1:02 am
=>

Suppose W is the total amount of work required to do the job and that RA and RB are the work rates of machines A and B, respectively.
Then the original condition tells us that RB = (1/2)RA.

Since machine A worked on the job for 6 hours, 1/4 of the job has been done, and (3/4)W is left.
The time T that machine B takes to complete the job is T = (3/4)W / RB = (3/4)W / (1/2)RA = (6/4)W/RA = (6/4)*24 = 36.

Therefore, the answer is E.

Answer: E
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