Question

An inlet pipe can fill a swimming pool in 9 hours and an outlet pipe can empty the pool in 12 hours. Through an error, both pipes are left open. How long will it take to fill te pool?

Answer 1

Answer:

36 hours.

Step-by-step explanation:

Let x represent time taken by both pipes to fill the tank.

We have been given that an inlet pipe can fill a swimming pool in 9 hours. So part of pool filled by inlet pipe in one hour would be $\frac{1}{9}$.

We are also told that an outlet pipe can empty the pool in 12 hours. The part of pool emptied by outlet pipe in one hour would be $\frac{1}{12}$.

Sine the time taken by both pipes to fill the tank is x hours, so part of pool filled by both pipes in one hour would be $\frac{1}{x}$.

We will get an equation using our given information as:

$\frac{1}{x}=\frac{1}{9}-\frac{1}{12}$

Let us solve for x.

$\frac{1}{x}=\frac{1*12}{9*12}-\frac{1*9}{12*9}$

$\frac{1}{x}=\frac{12}{108}-\frac{9}{108}$

$\frac{1}{x}=\frac{12-9}{108}$

$\frac{1}{x}=\frac{3}{108}$

Cross multiply:

$3x=108$

$\frac{3x}{3}=\frac{108}{3}$

$x=36$

Therefore, it will take 36 hours for both pipes to fill the tank.