Question 143381
Pipe A can fill a tank in 2 hours and Pipe B can fill it in half the time it takes
 Pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool.
 How much time is required for Pipe C to empty the tank?
:
Let t = time required for Pipe C to empty the tank:
:
It says, "Pipe B can fill it in half the time it takes Pipe C to empty it."
therefore:
Let .5t = time for Pipe B to fill the tank
:
Let the full pool = 1
:
Filling is positive, emptying is negative:
:
{{{1.5/2}}} + {{{1.5/.5t}}} - {{{1.5/t}}} = 1
Multiply equation 2t, to get rid of the denominators:
1.5t + 1.5(4) - 1.5(2) = 2t(1)
:
1.5t + 6 - 3 = 2t
:
1.5t - 2t = +3 - 6
:
-.5t = -3
t = {{{(-3)/(-.5)}}}
t = +6 hrs for the pipe to empty a full pool
:
:
Check solution using original equation:
{{{1.5/2}}} + {{{1.5/3}}} - {{{1.5/6}}} = 
.75 + .5 - .25 = 1; confirms our solution