Solve the problem and answer the question.
-BJ can overhaul a boat's diesel inboard engine in 15 hours. His apprentice takes 30 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency?
A) 4 hr
B) 45 hr
C) 10 hr
D) 6 hr

Question

Quizplus · Accepted Answer

Let's assume that the job is to overhaul one engine completely. 
BJ's rate of work = 1/15 of the job per hour
Apprentice's rate of work = 1/30 of the job per hour

When they work together, their rates of work are additive:
Rate of work when working together = BJ's rate of work + Apprentice's rate of work
= 1/15 + 1/30 (LCM of 15 and 30 is 30)
= 2/30 + 1/30
= 3/30
= 1/10 of the job per hour

Therefore, they can overhaul the engine working together in 10 hours:
time = job/rate of work = 1 / (1/10) = 10 hours.

So, the answer is C) 10 hr. BJ can complete 1/15 of the job in 1 hour.
His apprentice can complete 1/30 of the job in 1 hour.
Together they can complete (1/15 + 1/30) of the job in 1 hour.
Simplifying, (1/15 + 1/30) = 1/10.
Therefore, they can complete the job in 10 hours working together.

Solve the Problem and Answer the Question