Problem Solving

John has to hammer 100 railroad spikes for a new line his company is building. Working at a constant rate, he can hammer 8 spikes per hour. When he is halfway done, his coworker Paul begins working at the same constant rate. Compared to John completing all the work alone, how many hours are saved with Paul's help?

A. 5/2
B. 23/8
C. 25/8
D. 17/4
E. 25/4

If John completed the entire task by himself, the time would be 100/8 --> 25/2, or 12 and 1/2 hrs.

He would be halfway done after 6 and 1/4 hrs, and there would be 50 spikes remaining.

If he and Paul work together at the same rate for the remaining 50 spikes, their combined rate would be 16 spikes per hour.
The time that it would take them would be 50/16 --> 25/8, or 3 and 1/8 hrs.

If we add that to the 6 and 1/4 hrs that John already spent, the 100 spikes now took a total of 9 and 3/8 hrs (or 75/8).

To find out how many hours are saved, subtract:
25/2 - 75/8
100/8 - 75/8 = 25/8

The answer is C.