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Machine A can do a job in 24 hours at a constant rate and ma

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Machine A can do a job in 24 hours at a constant rate and ma

by Max@Math Revolution » Fri Mar 11, 2016 5:05 am
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job in 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


* A solution will be posted in two days.
Last edited by Max@Math Revolution on Sun Mar 13, 2016 5:11 am, edited 2 times in total.
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by regor60 » Fri Mar 11, 2016 6:14 am
This post is unintelligible
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by jain2016 » Fri Mar 11, 2016 7:53 am
Machine A can do a job in 24 hours at a constant rate and machine A do the job in 8 hours.



How come Machine A can do the job in 24 hours and 8 hours?


Please explain.

Thanks,

SJ
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by DavidG@VeritasPrep » Sat Mar 12, 2016 5:43 am
jain2016 wrote:
Machine A can do a job in 24 hours at a constant rate and machine A do the job in 8 hours.



How come Machine A can do the job in 24 hours and 8 hours?


Please explain.

Thanks,

SJ
I suspect the question should be worded as follows:

Machine A can do a job in 24 hours at a constant rate. Machine B works at 2/3 the rate of machine A. If machine A works alone for 8 hours, and then stops, how long will it take Machine B, working alone, to complete the rest of the job?
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by Max@Math Revolution » Sun Mar 13, 2016 5:11 am
Sorry for the confusion. I have revised the question.
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by Max@Math Revolution » Sun Mar 13, 2016 9:19 pm
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


Power of Machine A=W/24hrs. Since Machine A does the job for 8 hours, which becomes (W/3)/8hrs and 2W/3 is left. However, as power of Machine B is 2/3 of Machine A, power of B is (2/3)(W/24hrs)=(2W/3)/24hrs. Eventually, it takes 24 hours for Machine B to do the rest of the job.
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by DavidG@VeritasPrep » Mon Mar 14, 2016 5:14 am
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs
We can also use a bit of logic here. If Machine A works for 8 hours, it will do 8/24 = 1/3 of the job, leaving 2/3 of the job for B to do.

Well, if B is working at 2/3 the rate of A, and it has to do 2/3 of the job, it will take B the same amount of time to complete the rest of the job as it would have taken A to complete the full job. We know it takes A 24 hours to do the full job, so the answer is C.
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by GMATGuruNY » Mon Mar 14, 2016 5:23 am
Max@Math Revolution wrote:Machine A can do a job in 24 hours at a constant rate. If Machine A does the job in 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs
Let A's rate = 3 widgets per hour.
Since A takes 24 hours to complete the job, the job = rt = 3*24 = 72 widgets.

In 8 hours, the work completed by A = rt = 3*8 = 24 widgets.
Remaining work = 72-24 = 48 widgets.

Since B works at 2/3 of A's rate, B's rate = (2/3)(3) = 2 widgets per hour.
Time for B to produce the remaining 48 widgets = w/r = 48/2 = 24 hours.

The correct answer is C.
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by Jeff@TargetTestPrep » Tue Jan 02, 2018 10:29 am
Max@Math Revolution wrote:Machine A can do a job in 24 hours at a constant rate. If Machine A does the job in 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs
The rate of machine A is 1/24, so in 8 hours 1/3 of the job is completed, and thus 2/3 of the job is left to be completed.

If the rate of machine B is 2/3 that of machine A, then the rate of machine B is (2/3)(1/24) = 1/36.

Thus, it will take machine B (2/3)/(1/36) = 2/3 x 36 = 24 hours to complete the rest of the job.

Answer: C

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