SOLUTION: A pool has 1 intake pipe and 3 drainage pipes. It takes 20 minutes to fill up the pool. If 1 drainage pipe is used, it takes 45 minutes to drain the pool. Now 2/3 of the pool is fi

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Question 1163890: A pool has 1 intake pipe and 3 drainage pipes. It takes 20 minutes to fill up the pool. If 1 drainage pipe is used, it takes 45 minutes to drain the pool. Now 2/3 of the pool is filled. If all 4 pipes are turned on, how long does it take to have 2/5 of the pool filled?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The intake pipe fills 1/20 of the pool each minute.

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.

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.

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.

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.

ANSWER: 16 minutes