SOLUTION: It takes 9 hours for pump A to fill a tank alone. Pump B takes 15 hours to fill the same tank alone. If pumps A,B, and C are used, the tank fills in 5 hours. How long does it take

Question 584389: It takes 9 hours for pump A to fill a tank alone. Pump B takes 15 hours to fill the same tank alone. If pumps A,B, and C are used, the tank fills in 5 hours. How long does it take pump C to fill the tank?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
It takes 9 hours for pump A to fill a tank alone. Pump B takes 15 hours to fill the same tank alone. If pumps A,B, and C are used, the tank fills in 5 hours. How long does it take pump C to fill the tank?
.
Let c = time (hours) it takes for pump C to fill tank
then
5(1/9 + 1/15 + 1/c) = 1
5/9 + 5/15 + 5/c = 1
5/9 + 1/3 + 5/c = 1
multiplying both sides by 9c:
5c + 3c + 45 = 9c
8c + 45 = 9c
45 hours = c

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