Question
Pipe A can fill a tank in 8 hours, while pipe B can
empty the full tank in 12 hours. Both pipes are opened together. After how many hours should pipe B be closed so that the tank is exactly full in 10 hours?Solution
Let B be open for x hours. Rates: A = 1/8 per h, B = −1/12 per h Work done = x(1/8 − 1/12) + (10 − x)(1/8) = 1 1/8 − 1/12 = 1/24 So: x/24 + (10 − x)/8 = 1 Multiply 24: x + 3(10 − x) = 24 x + 30 − 3x = 24 −2x = −6 → x = 3 So B should be closed after 3 hours.
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