# A faucet can fill a sink in 3 minutes. It takes 2 times as long for the drain to empty the sink. How long will it take to fill the sink if the drain is open and the faucet is on?

May 19, 2018

$6$ minutes time will be required to fill the sink,when both
the faucet and drain are open.

#### Explanation:

Let the volume of sink is $v$ . The sink is filled in $3$ minutes.

Therefore In $1$ minute $\frac{1}{3}$ part of sink is filled up.

The sink is drained out to empty in $3 \cdot 2 = 6$ minutes.

Therefore In $1$ minute $\frac{1}{6}$ part of sink is emptied.

When both the faucet and drain is open the sink fills

$\frac{1}{3} - \frac{1}{6} = \frac{1}{6}$ part in one minute. Therefore to fill

completely required time is $\frac{1}{\frac{1}{6}} = 6$ minutes ,when both

the faucet and drain is open [Ans]