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?
13 1/3 minutes
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:
Where the 1 is a full sink. Now, we solve for x: