Question 270702
Let x=time it takes for tank to overflow when both pipes are open and the tank is empty
When both pipes are open the tank fills at the rate of 1/x tank per min

Inlet pipe fills at the rate of 1/10 tank per min
drain empties at the rate of 1/12 tank per min

So, our equation to solve is:
1/10 - 1/12=1/x  multiply each term by 60x
6x-5x=60
x=60 min--------------time it takes for tank to overflow when both pipes are open and the tank is empty


CK 
in 60 min inlet pipe fills (1/10)*60 or 6 tanks
in 60 min drain lets out (1/12)*60 or 5 tanks
So in 60 min we have a net gain of 1 tank---any more water and it overflows


Hope this helps---ptaylor