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Three machines, A, B, and C, can complete a certain

tagged by: M7MBA

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Three machines, A, B, and C, can complete a certain

Thu Mar 01, 2018 6:33 am
Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2

The OA is the option B.

Experts, may you help me here? I am confused. What formulas should I set here?

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GMATGuruNY GMAT Instructor
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Thu Mar 01, 2018 10:24 am
M7MBA wrote:
Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2
Let the task = the LCM of 10, 4 and 5 = 20 units.
Since A takes 10 hours to complete the 20-unit task, A's rate = w/t = 20/10 = 2 units per hour.
Since B takes 4 hours to complete the 20-unit task, B's rate = w/t = 20/4 = 5 units per hour.
Since C takes 5 hours to complete the 20-unit task, C's rate = w/t = 20/5 = 4 units per hour.
In 1 hour, the work produced by A+B+C = 2+5+4 = 11 units.
Remaining work = 20-11 = 9 units.
Since C's rate = 4 units per hour, the time for C to produce the remaining 9 units = w/r = 9/4 hours.

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Thu Mar 01, 2018 10:24 am
Hi M7MBA,

We're told that three Machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively and that all 3 machines worked together for 1 hour and then STOP. We're asked for the number of hours it would then take Machine C to complete the job on its own. Since we have 3 entities working on a task together, we can convert their work rates into 'fraction of the job completed per hour'...

Machine A = 10 hours to complete a job alone = 1/10 of the job completed per hour.
Machine B = 4 hours to complete a job alone = 1/4 of the job completed per hour.
Machine C = 5 hours to complete a job alone = 1/5 of the job completed per hour.

Thus, after 1 hour is done, a total of 1/10 + 1/4 + 1/5 = 2/20 + 5/20 + 4/20 = 11/20 of the job is done

This means that 1 - 11/20 = 9/20 of the job still has to be completed. Machine C completes 4/20 of the job each hour, so it would take (9/20) / (4/20) = 9/4 hours for Machine C to complete the job.

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Scott@TargetTestPrep GMAT Instructor
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Fri Mar 02, 2018 10:02 am
M7MBA wrote:
Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2
The combined rate of A, B, and C is:

1/10 + 1/4 + 1/5 = 2/20 + 5/20 + 4/20 = 11/20. So if all the machines work for 1 hour, 11/20 of the job is completed, and 9/20 is left to be completed.

Thus, it would take machine C (9/20)/(1/5) = 45/20 = 9/4 hours to complete the job.

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