Working alone at its constant rate, machine A can complete a job in 24

Question

Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs

A. 12hrs 
B. 16hrs 
C. 24hrs 
D. 32hrs 
E. 36hrs

JeffTargetTestPrep · Accepted Answer

The rate of machine A is 1/24, and the rate of machine B is 1/48.

After machine A has worked for 6 hours, 1/24 x 6 = 6/24 = 1/4 of the job has been completed, so machine B needs to complete the remaining 3/4 of the job.

Thus, it takes machine B a total of (3/4)/(1/48) = (48 x 3)/4 = 12 x 3 = 36 hours to complete the job.

Answer: E

BrentGMATPrepNow · Answer

Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A.   
So, it must take Machine B 48 hours to complete the job.

Now let's  assign a nice value  to the job. That is, we'll assign a value that works well with 24 hours and 48 hours. 
Let's say that the entire job consists of making a total of  48  widgets

If it take Machine A 24 hours to make  48  widgets, then machine A's RATE = 2 widgets per HOUR
If it take Machine B 48 hours to make  48  widgets, then machine B's RATE = 1 widget per HOUR

If machine A works on the job for 6 hours . . .   
At a rate of 2 widgets per HOUR, machine A can make  12  widgets in 6 hours
So, the amount of work remaining =  48  widgets -  12  widgets = 36 widgets

. . . and machine B completes the job, how long does it take machine B to finish the job?   
Machine B must make the 36 widgets
Machine B's RATE = 1 widget per HOUR
Time = output/rate = 36/1 = 36

It will take machine B 36 hours to complete the job.

Answer: E

Cheers,
Brent

Hero8888 · Answer

Dear MathRevolution,

Please check the answer options. As the GMATPrepNow above, I have got 36 h (E), but not 24(C) as you refer to. Thanks.

MathRevolution · Answer

=>

Suppose W is the total amount of work required to do the job and that R A  and R B  are the work rates of machines A and B, respectively.
Then the original condition tells us that R B  =  (\frac{1}{2}) R A .

Since machine A worked on the job for 6 hours,  \frac{1}{4}  of the job has been done, and  (\frac{3}{4}) W is left.
The time T that machine B takes to complete the job is T = (3/4)W / R B  = (3/4)W / (1/2)R A  = (6/4)W/R A  =  (\frac{6}{4}) *24 = 36.

Therefore, the answer is E.

Answer: E

AkshdeepS · Answer

Rate of A = 1/24

So, Rate of B = 1/2 * 1/24 = 1/48

Work done by A in 6 hours = 6*1/24 = 1/4

Remaining work done = 1 - 1/4 = 3/4

Time taken by B to complete the work = W/R

= 3/4 * 48/1

= 3*12

= 36 hrs

(E)

smritisingh8 · Answer

A did 25% job.

75% remains for which B will take twice of 75% of 24

.75 x 24 x 2 = 36

E.

Sent from my SM-T285 using  GMAT Club Forum mobile app

Abhishek009 · Answer

Time required by B to complete the work is 48 Hours & Time required by A to complete the work is 24 Hours.

Let the total work be 48 Units

So, Efficiency of A is 2 Units/Hr & Efficiency of B is 1 Units/Hr

Work completed by A in 6 Hours is 2*6 = 12 Units ; Work left is 48 - 12 = 36 Units....

So, Time required to complete the remainig work by B is 36 Hours, Answer must be (E)

Fdambro294 · Answer

Rate of B is HALF Rate of A

Means that B is Half as efficient as A

For a constant output of work, rate of work is inversely proportional to time needed to complete the work

So B will take TWICE as Long as A for any given output of work.

A takes 6 hours to complete (1/24) (6) = 6/24 = 1/4th of job

(3/4) of Job remains

If A takes 6 hours ————> to do (1/4) of job

Then B takes TWICE as long: 12 hours ———> to do (1/4) of job

But, B must complete the remaining work: the (3/4) of the job remaining

Since each (1/4) of job takes B 12 hours:

(12) + (12) + (12) = 36 hours

*E*

Posted from my mobile device

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Working alone at its constant rate, machine A can complete a job in 24

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