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27september2010

Pool Problem Solution

A swimming pool has four faucets. The first can fill the entire pool with water in two days, the second in three days, the third in four days, and the last one can fill the pool in 6 hours.
How long will it take to fill the pool using all 4 faucets together?

Solution:


Because there are 24 hours in one day, in one hour fills the first tap 1/48, the second tap 1/72, the third tap 1/96 and the fourth tap fills 1/6 of the reservoir. That is all together (6+4+3+48) / 288 = 61/288. The reservoir will be full in 288/61 hours, which is 4 hours 43 minutes and about 17 seconds.