# A faucet can fill a sink in 5 minutes while a drain will empty the same sink in 8 minutes. If the faucet is turned on and the drain is left open, how long will it take to fill the sink?

Mar 15, 2018

13 1/3 minutes

#### Explanation:

I wrote this as a function of fractions. If filling is treated as a positive value, broken into fifths (5 min per fill), and drainage is a negative value, broken into eighths, the equation looks like this:

$\frac{x}{5} - \frac{x}{8} = 1$

Where the 1 is a full sink. Now, we solve for x:

$\frac{x}{5} \times \frac{8}{8} - \frac{x}{8} \times \frac{5}{5} = 1 \Rightarrow \frac{8 x}{40} - \frac{5 x}{40} = 1$

$\frac{3 x}{40} \times 40 = 1 \times 40 \Rightarrow 3 x = 40$

$\textcolor{red}{x = \frac{40}{3} = 13 \frac{1}{3}}$