Question 286901
Let x=amount of time it takes both pipes to fill the chamber if the drain is left open
With the drain open, both pipes fill at the rate of 1/x chamber per min
First pipe fills at the rate of 1/4 chamber per min
2nd pipe fills at the rate of 1/6 chamber per min
But the drain empties at the rate of 1/12 chamber per min
So, with the drain open, both pipes fill at the rate of
1/4 + 1/6 - 1/12 chamber per min. Our equation to solve then is:
1/4 + 1/6 - 1/12=1/x   multiply each term by 12x
3x+2x-x=12
4x=12
x=3 min----amount of time it takes both pipes to fill the chamber if the drain is left open

CK
in 3 min first pipe fills (1/4)*3=3/4 chamber
in 3 min 2nd pipe fills (1/6)*3=1/2 chamber 
in 3 min drain empties (1/12)*3=1/4 chamber
3/4 + 1/2 - 1/4 should equal 1 (1 chamber, that is)
3/4 + 2/4 -1/4=4/4=1
1=1

Hope this helps---ptaylor