Question

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?

Answer 1

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:

`x/5-x/8=1`

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

`x/5xx8/8-x/8xx5/5=1 rArr (8x)/40-(5x)/40=1`

`(3x)/40xx40=1xx40 rArr 3x=40`

`color(red)(x=40/3=13 1/3)`