Rate of 1st input pipe = 1/10
Rate of 2nd input pipe = 1/8

Rate of drain = 1/6

Combined rate of 2 input pipes = 1/10+1/8
= 9/40

For the first 1/2 of the work the 2 input pipes and the drain were open so we can calculate this time (time taken for the tank to get half full)

rate * time = work

(9/40 - 1/6) * t = 1/2

time = 60/7 (1)

Now the drain is closed and the 2 input pipes work at their combined rates to fill the other 1/2 of the tank

rate * time = work

9/40 * time= 1/2

time = 20/9 (2)


Total time = (1) + (2)

= 60/7 + 20/9
= 10.8