Question 1163890
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The intake pipe fills 1/20 of the pool each minute.<br>
Each drain pipe empties 1/45 of the pool each minute; the three drain pipes together empty 3/45 = 1/15 of the pool each minute.<br>
If all 4 pipes are open, the fraction of the pool that is emptied each minute is 1/15-1/20 = 4/60-3/60 = 1/60.<br>
Starting with the pool 2/3 full and going until it is 2/5 full, the fraction of the pool that is emptied is 2/3-2/5 = 10/15-6/15 = 4/15.<br>
The number of minutes required to empty 4/15 of the pool at the rate of 1/60 of the pool per minute is (4/15)/(1/60) = (16/60)/(1/60) = 16.<br>
ANSWER: 16 minutes<br>