# math

Three water pipes are used to fill a swimming pool. The 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. If all 3 pipes are opened at the same time, how long will it take all 3 together to fill the pool?

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1. rates of each of the pipes are 1/8 pools per hour, 1/12 pools per hour, and 24 pools per hour.
the combined rate would be
(1/8 + 1/12 + 1/24) pools per hour
= 1/4 units per hour

Time using combined rate = 1 pool/(1 pool/4) hours
= 4 hours

(the "pool" unit canceled)

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2. a large pipe can empty a pool in 6hours and a smaller pipe can empty the same pool in 9 hours. how long will it take both pipes to empty the pool.

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