Question 1170011
<br>
Each minute, the drain empties 1/3 of the sink while the faucet fills 1/5 of the tank.<br>
The fraction of the sink that empties in one minute is then {{{(1/3) - (1/5) = (5/15) - (3/15) = (2/15)}}}.<br>
The number of minutes it will take to empty the sink is {{{1/(2/15) = 1*(15/2) = 15/2 = 7.5}}}<br>
ANSWER: 7.5 minutes<br>
For students who dislike working with fractions, here is a different method for solving problems like this.<br>
Consider a time period of 15 minutes, which is the least common multiple of the times for filling and emptying the sink.<br>
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.<br>
And that means the two together could empty the one tank in half as much time -- 15/2 = 7.5 minutes.<br>