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Machine A can do a job in 12 hours at a constant rate and machine A do

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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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New post 03 Nov 2016, 01:28
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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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New post 03 Nov 2016, 01:38
1
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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New post 03 Nov 2016, 09:06
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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

Hence, Correct 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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New post 07 Nov 2016, 00:51
==> 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.

Answer: 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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New post 06 Mar 2018, 03:52
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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? :dazed
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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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New post 06 Mar 2018, 08:55
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

Answer 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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New post 19 Mar 2018, 03:29
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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New post 18 Jun 2018, 06:50
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

Answer A


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. :-D
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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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New post 20 Jun 2018, 17:03
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.

Answer: A
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Re: Machine A can do a job in 12 hours at a constant rate and machine A do &nbs [#permalink] 20 Jun 2018, 17:03
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