Question 206797
Let x=amount of time it takes to empty the tank when both pipes are left open
Then, with both pipes open ,the tank empties at the rate of 1/x tank per min

Drain pipe empties at the rate of 1/30 tank per min
Inlet pipe fills at the rate of 1/45 tank per min
Then, with both pipes open ,the tank empties at the rate of 1/30-1/45 tank per min 

So, our equation to solve is
1/30-1/45=1/x  multiply each term by 90x
3x-2x=90
x=90 min------------------amount of time to empty tank when both pipes are left open

CK

In 90 min, inlet pipes pours in 90(1/45) or 2 tanks of water
In 90 min, drain pipe drains 90(1/30) or 3 tanks of water
So the two tanks of water poured in by the inlet pipe in 90 min plus the full tank that was already there equals the 3 tanks that were emptied by the drain pipe.

Hope this helps---ptaylor