SOLUTION: 2) Pipe A can fill a tank in 4hr. Pipe B can fill the tank in 9hr less than the time it takes pipe C, a drain pipe, to empty the tank. When all three pipes are open, it takes 2hr

Question 127989: 2) Pipe A can fill a tank in 4hr. Pipe B can fill the tank in 9hr less than the time it takes pipe C, a drain pipe, to empty the tank. When all three pipes are open, it takes 2hr to fill the tank. How much time is required for pipe C to empty the tank if pipes A and B are closed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Pipe A can fill a tank in 4 hr. Pipe B can fill the tank in 9 hr less than the time it takes pipe C, a drain pipe, to empty the tank. When all three pipes are open, it takes 2 hr to fill the tank. How much time is required for pipe C to empty the tank if pipes A and B are closed?
:
Pipe C's draining time = x (when Pipes A & B are closed)
:
Pipes A's filling time = 4 hr (given)
:
Pipe B's filling time = (x-9) (Given as 9 hrs less than C)
:
Let the full tank = 1
:
Filling is +, draining is -
:
The equation when all three are open for 2 hrs:
+ - = 1
:
Multiply the equation by 4x(x-9) to get rid of the denominators:
4x(x-9)* + 4x(x-9)* - 4x(x-9)* = 4x(x-9)(1)
Cancel out the denominators and you have:
x(x-9)*2 + 4x(2) - 4(x-9)*2 = 4x(x-9)
:
2x^2 - 18x + 8x - 8x + 72 = 4x^2 - 36x
:
2x^2 - 4x^2 - 18x + 36x + 72 = 0
:
-2x^2 - 18x + 72 = 0
:
x^2 - 9x - 36 = 0; Divide by -2; simplifies and changes the signs
Factors to
(x + 3) (x - 12) = 0
Positive solution
x = 12 hrs for the the drain to empty the tank with A & B closed
:
;
Check solution (B's fill time will be 12-9 = 3 hrs)
+ - =
+ - = = 1

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