John has to hammer 100 railroad spikes for a new line his co

BTGmoderatorDC wrote: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

OA C

Source: Veritas Prep

Given that John can hammer 8 spikes per hour, time needed to hammer 100 spikes, working alone = 100/8 = 25/2 hours.

Since John alone hammered half the number of spikes (100/2 = 50), the number of hours John worked alone = 1/2 of 25/2 = 25/4 hours

Now John's coworker Paul also joined him and his rate of work is the same as that of John, the number of hours required to hammer the remaining 50 spikes = 1/2 of 25/4 = 25/8 hours

Thus, the actual number of hours spent to hammer 100 spikes = 25/4 + 25/8 = 75/8 hours

Time saved = 25/2 – 75/8 = 25/8 hours

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote: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 were to work alone, it would take him 100/8 hours.

For John to complete half the job, it takes him 50/8 hours. When his coworker Paul joins him, it takes them ½ x 50/8 = 50/16 hours to complete the remaining half of the job.

Thus, it takes a total of 50/8 + 50/16 = 100/16 + 50/16 = 150/16 = 75/8 hours to complete the entire job.

Thus, the number of hours saved is 100/8 - 75/8 = 25/8 hours.

Answer: C

BTGmoderatorDC wrote: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

OA C

Source: Veritas Prep

If John were to work alone, it would take him 100/8 hours.

For John to complete half the job, it takes him 50/8 hours. When his coworker Paul, who works at the same rate, joins him, it takes them ½ x 50/8 = 50/16 hours to complete the remaining half of the job.

Thus, it takes a total of 50/8 + 50/16 = 100/16 + 50/16 = 150/16 = 75/8 hours to complete the entire job.

Thus, the number of hours saved is 100/8 - 75/8 = 25/8 hours.

Answer: C