Question 206410
Let x=amount of time it takes both pumps to fill the pool when working together
So both pumps fill at the rate of 1/x tank per hour
First pump fills at the rate of 1/9 tank per hour
Second tank fills at the rate of 1/6 tank per hour
Together, they fill at the rate of 1/9 +1/6 tank per hour
So, our equation to solve is:
1/9 + 1/6=1/x  multiply each term by 18x
2x+3x=18
5x=18 
x=3 3/5 hours or 3h 36m--------------time it takes both tanks working together 

CK
In 3 3/5 hours, tank one fills (1/9)(18/5)=2/5 of the tank
In 3 3/5 hours  second tank fills (1/6)(18/5)=3/5 of the tank
2/5 + 3/5 =5/5 or the whole tank

Hope this helps---ptaylor