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Question

Two pipes together can fill a tank in 12 hours. If the first pipe can fill the tank 10 hours faster than the second then how many hours will the second pipe take to fill the tank?

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Solution

Let the time required to fill the tank by second pipe be x hours.
Then, the time required to fill the tank by first pipe is (x − 10) hours.

Given:
Two pipes together can fill a tank in 12 hours.

According to the question,

1x+1x-10=112x-10+xxx-10=1122x-10x2-10x=11224x-120=x2-10xx2-10x-24x+120=0x2-34x+120=0x2-30x-4x+120=0xx-30-4x-30=0x-30x-4=0x=30, 4But x-10 is the time required by the first pipe to fill the tank, which is always positive.Thus, x=30 and x4


Hence, the second pipe will take 30 hours to fill the tank.

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