Chapter A.8, Problem 50AYU

To determine

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

Answer to Problem 50AYU

1 and $\frac{3}{4}$ 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 $\frac{1}{5}=$ the work that the 5 hp pump does each hour (if it can do the whole job in 5 hours, it is doing $\frac{1}{5}$ of the job each hour.

Let $\frac{1}{8}=$ the work that the 2 hp pump.

Therefore,

$\frac{1}{5}+\frac{1}{8}=\frac{8}{40}+\frac{5}{40}$ or $\frac{13}{40}$ of the job each hour.

So in 2 hours, they have completed $\left(2\right).\frac{13}{40}$ (or) $\frac{13}{20}$.

This means that there is only $\frac{7}{20}$ of the job left to do.

We know that the rate of work $*$ time $=$ amount of work completed so, $\frac{1}{5}\text{(time)}=\frac{7}{20}$.

Therefore time $=\frac{7}{4}$ or 1 and $\frac{3}{4}$ hours.