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An inlet pipe on a swimming pool can be used to fill the pool in 12 hours. The drain pipe can be used to empty the pool in 48 hours. If the pool is 1/4 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
An inlet pipe on a swimming pool can be used to fill the pool in 12 hours. The drain pipe can be used to empty the pool in 48 hours. If the pool is 1/4 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
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the inlet fills 1/12 of the pool per hour
teh drain lets out 1/48 of the pool per hour
the net fill rate if they're both operating is (1/12 - 1/48) per hour
= 4/48 - 1/48 = 3/48 = 1/16 of the pool per hour
if 1/4 is filled, then 3/4 is left to fill
at 1/16 per hour, this will take (3/4) / (1/16) = (3/4) * (16/1) = 12 hours
it will take 12 hours to fill the remaining 3/4 of the pool with both the drain and fill pipes open
teh drain lets out 1/48 of the pool per hour
the net fill rate if they're both operating is (1/12 - 1/48) per hour
= 4/48 - 1/48 = 3/48 = 1/16 of the pool per hour
if 1/4 is filled, then 3/4 is left to fill
at 1/16 per hour, this will take (3/4) / (1/16) = (3/4) * (16/1) = 12 hours
it will take 12 hours to fill the remaining 3/4 of the pool with both the drain and fill pipes open