Bob Can Overhaul A Boat's Diesel Inboard Engine In 15 Hours

Bob Can Overhaul A Boats Diesel Inboard Engine In 15 Hours His A

Bob 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. 10 hr b. 45 hr c. 6 hr d. 4 hr

Paper For Above instruction

Properly functioning engines are essential for the safe and efficient operation of boats, and understanding the dynamics of maintenance tasks like engine overhaul is crucial in marine operations. This paper tackles a problem involving the rates at which Bob and his apprentice can overhaul a boat's diesel inboard engine and how their combined efforts affect the overall time taken to complete the task.

Given that Bob can complete the overhaul in 15 hours and his apprentice in 30 hours, we analyze their individual work rates and combine these to determine the total time required working together. The calculation proceeds by converting individual times into work rates, adding these rates, and then reverting to find the combined time.

Bob's work rate is 1/15 engines per hour, while the apprentice's is 1/30 engines per hour. Adding these yields:

(1/15) + (1/30) = (2/30) + (1/30) = 3/30 = 1/10 engines per hour.

This combined rate indicates that working together, they can complete 1/10 of the job per hour. Taking the reciprocal gives the total time:

Total time = 1 / (1/10) = 10 hours.

Therefore, working together, Bob and his apprentice would complete the overhaul in 10 hours, matching option a) 10 hr.

In practical terms, this calculation underscores the efficiency gains achieved through teamwork in mechanical maintenance operations. It reflects the additive nature of work rates, where parallel efforts contribute to faster project completion.

Understanding such problem-solving techniques is vital in mechanical and engineering contexts, especially in industries like marine engineering, where time-efficient repairs can significantly impact operational schedules and safety.

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