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1. Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all three pipes are open, empty tanks become full in one hour. The capacity of the tank (in gallons) is:

A. 800 gallons

B. 600 gallons

C. 500 gallons

D. 400 gallons

Solution:

Let capacity of the tank = x gallons;
Part of the tank filled in 1 minute

\begin{aligned} = \frac{x}{24} + \frac{x}{40} - 30 \\ Or, \frac{x}{24} + \frac{x}{40} - 30 = \frac{x}{60} \\ Or, \frac{x}{24} + \frac{x}{40} - \frac{x}{60} = 30 \\ Or, \frac{10 x + 6 x - 4 x}{240} = 30 \\ Or, 12 x = 30 \times 240 \\ Or, x = 600 gallons \end{aligned}

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