SOLUTION: a sink can be filled from the faucet in 5 minutes. it takes only 3 minutes to empty the sink when the drain is open. if the sink is full and both the faucet and drain are open, how

Algebra ->  Finance -> SOLUTION: a sink can be filled from the faucet in 5 minutes. it takes only 3 minutes to empty the sink when the drain is open. if the sink is full and both the faucet and drain are open, how      Log On


   

Question 1170011: a sink can be filled from the faucet in 5 minutes. it takes only 3 minutes to empty the sink when the drain is open. if the sink is full and both the faucet and drain are open, how long will it take to empty the sink?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Each minute, the drain empties 1/3 of the sink while the faucet fills 1/5 of the tank.

The fraction of the sink that empties in one minute is then %281%2F3%29+-+%281%2F5%29+=+%285%2F15%29+-+%283%2F15%29+=+%282%2F15%29.

The number of minutes it will take to empty the sink is 1%2F%282%2F15%29+=+1%2A%2815%2F2%29+=+15%2F2+=+7.5

ANSWER: 7.5 minutes

For students who dislike working with fractions, here is a different method for solving problems like this.

Consider a time period of 15 minutes, which is the least common multiple of the times for filling and emptying the sink.

In 15 minutes, the faucet could fill the sink 15/5 = 3 times; in 15 minutes the drain could empty the sink 15/3 = 5 times. So in 15 minutes the faucet and drain together could empty the sink 5-3 = 2 times.

And that means the two together could empty the one tank in half as much time -- 15/2 = 7.5 minutes.