Work = Rate * Time
when Work = 1

1= Rate * Time
Rate = 1 / Time

Given,

A and B, operating simultaneously, can fill a certain tank in 6/5 hours
A + B = 1 / 6/5 = 5/6......I

A and C, operating simultaneously, can fill a certain tank in 3/2 hours
A + C = 1 / 3/2 = 2/3......II

B and C, operating simultaneously, can fill a certain tank in 2 hours
B + C = 1 / 2 = ..............III

Adding I, II and III

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

A, B, and C, operating simultaneously = 1/1 = 1

Thank you! The problem looks so simple when you think about it. I was unsuccessfully attempting to solve for each variable using the three equations and adding them up. As you can imagine, my methodology did not work.