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
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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?
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Pipe C's draining time = x (when Pipes A & B are closed)
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Pipes A's filling time = 4 hr (given)
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Pipe B's filling time = (x-9) (Given as 9 hrs less than C)
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Let the full tank = 1
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Filling is +, draining is -
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The equation when all three are open for 2 hrs: + - = 1
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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
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2x^2 - 4x^2 - 18x + 36x + 72 = 0
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-2x^2 - 18x + 72 = 0
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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
