Problem Solving - 49

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

Answer: E

1/A + 1/B = 5/6
1/B +1/C = 2/3
1/C + 1/A =1/2

Adding  all three equations above we get:

1/A + 1/B + 1/B +1/C + 1/C + 1/A = 5/6 + 2/3 + 1/2
2(1/A + 1/B + 1/C) = (5 + 4 + 3)/ 6 = 12/6
1/A + 1/B + 1/C = 12/6*2 = 1

=> Pumps A, B, and C, operating simultaneously will fill the tank in 1 hr