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Math Revolution GMAT Instructor V
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Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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Question Stats: 74% (02:04) correct 26% (02:10) wrong based on 219 sessions

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Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

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

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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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2
Machine A worked for 4 hours => completed 1/3rd of the work.
Machine B does the work at 2/3 rate of A => time taken by B to complete = $$\frac{3}{2} *12$$ = 18 hours.

B needs to complete 2/3rd of the work. Let time taken be x

$$\frac{1}{18} * x =\frac{2}{3}$$
x = 12

Option A
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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

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

Let total work be 36

Efficiency of A = 3

Efficiency of B = 2

A works for 4 hours so it completes 12 units, hence work left is 24 units

Since B does 24 units , time required by it is 24/2 = 12

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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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==> Machine A works for 12 hours, but only did 4 hours, which is 1/3 of the job. Then, 2/3 of the job remains. Since the power of B is 2/3 of A’s, it takes 12 hours for B to do the remaining job. Hence, the answer is A.

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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate but machine A do the job for 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

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

Isn't this wording more appropriated? Senior SC Moderator V
Joined: 22 May 2016
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Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

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

MvArrow , I got confused, too. I rewrote:

Machine A can do a job in 12 hours at a constant rate. Machine A works for 4 hours. Machine B, working at a constant rate, can do the same job at 2/3 of the rate of machine A. If machine B does the rest of the job alone, how many hours does it take for Machine B to finish?

Amount of work completed by Machine A?
Work = 1 job
Rate of A: $$\frac{1Job}{12hrs}=\frac{1}{12}$$
Time that Machine A worked: 4 hours
Amount of work, $$W,$$ that Machine A completes:
$$W = R * T$$
$$W=(\frac{1}{12} *4)=\frac{4}{12}=\frac{1}{3}$$
of Work finished

Work remaining for B:$$\frac{2}{3}$$

B's rate? B is slower than A
B's rate is $$\frac{2}{3}$$ the rate of (= multiply) A
B's rate: $$(\frac{1}{12}*\frac{2}{3})=\frac{2}{36}=\frac{1}{18}$$ = rate of B

Time needed for B to finish work remaining?
$$\frac{2}{3}$$ of work remains
$$R * T= W$$, so $$T = \frac{W}{R}$$

Time for B:$$\frac{\frac{2}{3}}{\frac{1}{18}}=(\frac{2}{3}*\frac{18}{1})=12$$ hours

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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

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

Please correct the wording here. What is the question trying to say?
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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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generis wrote:
MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

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

MvArrow , I got confused, too:
Machine A can do a job in 12 hours at a constant rate. Machine A works for 4 hours. Machine B, working at a constant rate, can do the same job at 2/3 the rate of machine A. If machine B does the rest of the job alone, how many hours does it take for Machine B to finish?

Amount of work completed by Machine A?
Work = 1 job
Rate of A: $$\frac{1Job}{12hrs}=\frac{1}{12}$$
Time that Machine A worked: 4 hours
Amount of work Machine A completes:
$$W = R * T$$
$$W = \frac{1}{12} * 4=\frac{4}{12}=\frac{1}{3}$$
of Work finished

Work remaining for B:$$\frac{2}{3}$$

B's rate? B is slower than A
B's rate is $$\frac{2}{3}$$ the rate of (= multiply) A
B's rate: $$(\frac{1}{12}*\frac{2}{3})=\frac{2}{36}=\frac{1}{18}$$ = rate of B

Time needed for B to finish work remaining?
$$\frac{2}{3}$$ of work remains
$$R * T= W$$, so $$T = \frac{W}{R}$$

Time for B:$$\frac{\frac{2}{3}}{\frac{1}{18}}=(\frac{2}{3}*\frac{18}{1})=12$$ hours

True... Wording of question is very poor. Hopefully GMAC never does such things. It is a relief that many have been confused by the wording, otherwise I was blaming myself. _________________
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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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MathRevolution wrote:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

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

The rate of Machine A is 1/12, and the rate of Machine B is 2/3 x 1/12 = 1/18.

Machine A works for 4 hours, so it completes 4 x (1/12) = 1/3 of the job.

When machine A stops working, 2/3 of the job remains to be finished by machine B. Thus, machine B works for (2/3)/(1/18) = 36/3 = 12 hours alone.

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Re: Machine A can do a job in 12 hours at a constant rate and machine A do  [#permalink]

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Confusing wording:
Machine A can do a job in 12 hours at a constant rate and machine A do the job in 4 hours. Re: Machine A can do a job in 12 hours at a constant rate and machine A do   [#permalink] 03 Dec 2019, 23:18
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