Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
Question
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Chapter A.8, Problem 50AYU
To determine

To find: How long will it take the larger pump to finish emptying the pool?

Expert Solution & Answer
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Answer to Problem 50AYU

1 and 3 4 hours will it take the larger pump to finish emptying the pool.

Explanation of Solution

Given:

A 5-horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2-hp pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool. After 2 hours, the 2-hp pump breaks down.

Calculation:

Let 1 5  = the work that the 5 hp pump does each hour (if it can do the whole job in 5 hours, it is doing 1 5 of the job each hour.

Let 1 8  = the work that the 2 hp pump.

Therefore,

1 5  +  1 8  =  8 40  +  5 40 or 13 40 of the job each hour.

So in 2 hours, they have completed ( 2 ) .  13 40 (or) 13 20 .

This means that there is only 7 20 of the job left to do.

We know that the rate of work * time = amount of work completed so, 1 5 (time) =  7 20 .

Therefore time =  7 4 or 1 and 3 4 hours.

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