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 tank in 2 hours. How many hours does it take pumps A, B and C, operating simultaneously, to fill the tank?
A)1/3
B)1/2
C)2/3
D)5/6
E)1
Let the pool = 18 units.
Rate for A+B = w/t = 18/(6/5) = 15 units per hour.
Rate for A+C = w/t = 18/(3/2) = 12 units per hour.
Rate for B+C = w/t = 18/2 = 9 units per hour.
Combining the rates:
(A+B) + (A+C) + (B+C) = 15+12+9 = 36.
2A + 2B + 2C = 36.
A+B+C = 18 units per hour.
Time for A+B+C to fill the pool = w/r = 18/18 = 1 hour.
The correct answer is
E.
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