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?

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Answer 1 · 2018-05-19T04:26:10

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

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

Therefore In $1$ minute $1/3$ part of sink is filled up.

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

Therefore In $1$ minute $1/6$ part of sink is emptied.

When both the faucet and drain is open the sink fills

$1/3-1/6 = 1/6$ part in one minute. Therefore to fill

completely required time is $1/(1/6)=6$ minutes ,when both

the faucet and drain is open [Ans]