Problem Solving

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 a certain tank in 2/3 hours; and pumps B and C, operating simultaneously, can fill a certain tank in 6/5 hours. How many hours does it take A, B, and C, operating simultaneously, to fill the tank?

Is the answer 12/19 hrs?

This question wasn't difficult but very very time consuming. I wonder if this would actually appear on the real GMAT exam...?

The answer would be 12/19 hours if the question is written correctly. However, if this is the GMAT prep question, I think the second 6/5 is supposed to be a different number.

This can be solved by breaking the given information to smaller pieces.
Like,

A+B = 5/6 (because, 1/6/5= 5/6)
A+C = 3/2
B+C = 5/6

Adding all the 3 equation gives,
2(A+B+C) = 5/6+3/2+5/6
2(A+B+C) = 19/6
A+B+C = 19/12

So time taken by 3 pumps can be written as 12/19