A water tank has three pipes. The first pipe fills the tank in 2 hours, the second pipe fills it in 3 hours, and the third empty pipe drains the full tank in 6 hours. If all three pipes are open simultaneously, how many hours will it take to fill the empty tank?
1.5 hours
In 1 hour, pipe 1 fills 1/2, pipe 2 fills 1/3, and pipe 3 drains 1/6. Net rate per hour = 1/2 + 1/3 - 1/6 = 3/6 + 2/6 - 1/6 = 4/6 = 2/3 of the tank. The time to fill is the reciprocal: 3/2 = 1.5 hours.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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