alex.gellatly wrote:Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the thank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank?
1/3
1/2
2/3
5/6
1
Thanks
Let tank = 6 liters.
Rate for A and B = w/t = 6/(6/5) = 5 liters per hour.
Rate for A and C = w/t = 6/(3/2) = 4 liters per hour.
Rate for B and C = w/t = 6/2 = 3 liters per hour.
Combining the rates above:
(A+B) + (A+C) + (B+C) = 5+4+3 = 12.
2A + 2B + 2C = 12.
A+B+C = 6 liters per hour.
Time for A+B+C = w/r = 6/6 = 1 hour.
The correct answer is
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