Problem Solving

Max@Math Revolution wrote:[GMAT math practice 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

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

Max@Math Revolution wrote:
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

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