Question

A pump can fill a swimming pool in 8 hours. The pool also has a drain that can empty the pool in 10 hours. If someone turns on the pump to fill the pool, but forgets to shut the drain, how long would it take for the pool to fill?

Answer 1

Answer:

40 hours will it take for the pool to fill.

Step-by-step explanation:

A pump can fill a swimming pool in 8 hours.

Work done by pump to fill in 1 hour is  $\frac{1}{8}$

The pool also has a drain that can empty the pool in 10 hours.

Work done by pump to drain in 1 hour is  $\frac{1}{10}$

If someone turns on the pump to fill the pool, but forgets to shut the drain.

Work done by both pipe in 1 hour is

$W=\frac{1}{8}-\frac{1}{10}$

$W=\frac{10-8}{80}$

$W=\frac{2}{80}$

$W=\frac{1}{40}$

Both pipe filled $\frac{1}{40}$ part of pool in hours = 1

Both pipe filled complete pool in hours = $\frac{1}{\frac{1}{40}}=40$

Therefore, 40 hours will it take for the pool to fill.