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Machine A and B

This topic has 4 expert replies and 1 member reply

Machine A and B

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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

Is there a strategic approach to this? Experts help please. Thanks

OA C

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lheiannie07 wrote:
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
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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lheiannie07 wrote:
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
Let the job = 72 widgets.

Since A takes 24 hours to complete the job, A's rate = w/t = 72/24 = 3 widgets per hour.
At a rate of 3 widgets per hour, the work produced by A in 8 hours = rt = 3*8 = 24 widgets.

Remaining work = 72-24 = 48 widgets.
Since B's rate is 2/3 of A's rate, B's rate = (2/3)(3) = 2 widgets per hour.
At a rate of 2 widgets per hour, the time for B to produce the remaining 48 widgets = w/r = 48/2 = 24 hours.

The correct answer is C.

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Post
lheiannie07 wrote:
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

Is there a strategic approach to this? Experts help please. Thanks

OA C
If machine A can complete the job in 24 hours, and it works for 8 hours, then it has completed 8/24 or 1/3 of the job, leaving 2/3 of the job for B to complete.

If Machine A's rate was 1 job/24 hours, or 1/24, and B's rate is 2/3 of this, then B's rate is (2/3) * (1/24) = 1/36.

If Machine B works for T hours at a rate of 1/36 and must complete 2/3 of a job, we get the following equation: (1/36) * T = 2/3 --> T = 24; The answer is C

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Post
lheiannie07 wrote:
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

Is there a strategic approach to this? Experts help please. Thanks

OA C
Another approach. If Machine A has worked for 8 hours, and it takes Machine A 24 hours to complete the job, it would take Machine A an additional 16 hours to finish the job alone.

Rate and Time have a reciprocal relationship. If B's rate is 2/3 of A's rate, then it would take B 3/2 of A's Time to complete the job. If it would have taken A 16 hours to complete the job, it would take B 16*(3/2) or 24 hours. The answer is C.

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Thank you so much for the solution, but is there an easier way to solve this?

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