Each valve a, b, and c, when open, releases water into a tank at its own constant rate. with all three valves open, the tank fills in 1 hour, with only valves a and c open it will take 1.5 hours, and with only valves b and c open it takes 2 hours. how many minutes will it take to fill the tank with only valves a and b open?

Time taken by A and B is 1.2 hr.

Explanation:

Given that

Time taken by tank when all(A+B+C) are open = 1 hr

Time taken by tank when A+C are open = 1.5 hr

Time taken by tank when B+C are open = 2 hr

If we treat as filling of tank is a work then

Work = time x rate

Lets take work is 1 unit

1 = 1(1/a+1/b+1/c)          ---------1

1 = 1.5(1/a+1/c)           ----------2

1 = 2(1/b+1/c)             --------3

From equation 1 and 3

1=1(1/a+1/2)

a=2

Form equation 2

1 = 1.5(1/2+1/c)

c=6

From equation 3

 1 = 2(1/b+1/6)  

b=3

So time taken by

A is alone to fill tank is 2 hr

B is alone to fill tank is 3 hr

C is alone to fill tank is 6 hr

So

Time taken by A and B is 1.2 hr.