Pipe question filling a water tank with the drain pipe open?

There are 2 inlet pipes for a large water tank and one drain pipe. Alone at full force, the first pipe can fill the tank in 10 hours. The second pipe can fill the tank in 8 hours. The drain pipe empties a full tank in 6 hours if neither is running. Suppose the tank is empty. Both pipes are running at full force. The drain pipe is open. When the tank is half full, the drain pipe is closed, and the inlet pipes contine running. HOw long will it take to completely fill the tank in this situation beginning with an empty tank?Pipe question filling a water tank with the drain pipe open?
Say the volume of a full tank is V


The flow rates for the first inlet, second inlet and drain pipe are


V / 10, V / 8, and -V / 6 (this assumes flow out of the drain pipe is constant which is not usually the case, but would have to be assumed since we don't have dimensions of the tank)


Setting up an equation with these flow rates to fill the first half of the volume (t is time in hours)


(V/8)t + (V/10)t - (V/6)t = V/2


Divide through by V, and use common denominator 120


(15t + 12t - 20t) / 120 = 1/2


Multiply both sides by 120


7t = 60


t = 60 / 7 = 8.57 hours to fill half the tank, and then when the drain valve closes the equation becomes


(V/8)t + (V/10)t = V/2


Divide through by V, common denominator 40


(5t + 4t) / 40 = 1/2


9t = 20


t = 20 / 9 = 2.22 hours to fill second half of tank.


Total time = 8.57 hours + 2.22 hours = 10.79 hours.