Carcass wrote:

A distillate flows into an empty 64-gallon drum at spout A and out of the drum at spout B. If the rate of flow through A is 2 gallons per hour, how many gallons per hour must flow out at spout B so that the drum is full in exactly 96 hours?

(A) \(\frac{3}{8}\)

(B) \(\frac{1}{2}\)

(C) \(\frac{2}{3}\)

(D) \(\frac{4}{3}\)

(E) \(\frac{8}{3}\)

Let x = rate at which water is flowing out from B

so Net rate =\(2 - x\)

SInce we know

Amount of work = Rate * time

or \(64 = (2-x) * 96\)

or \(64 = 192 - 96x\)

or\(x = \frac{128}{96} = \frac{4}{3}\)

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