2. Question: It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B used alone takes 8 hours to fill the same tank. We want to use three pumps: A, B and another pump C to fill the tank in 2 hours. What should be the rate of pump C? How long would it take pump C, used alone, to fill the tank?
Let the total capacity of the tank be C liters.
Fill rate of pump A, Fa = C/6 liters per hr
Fill rate of pump B, Fb = C/8 liters per hr
2 hrs x [Fa + Fb + Fc] = C => Fc = 5C/24 liters per hr
Let‘t’ be the time taken by only pump C to fill the tank.
‘t’ hrs x 5C/24 = C => t = 24/5 = 4.8 hrs
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