SOLUTION: Pipe A can fill a tank in 5 hours. Pipe B can fill the tank in 2 hours less time than it takes pipe C to empty it. With all pipes open it takes 3 hours to fill the tank. How long w
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-> SOLUTION: Pipe A can fill a tank in 5 hours. Pipe B can fill the tank in 2 hours less time than it takes pipe C to empty it. With all pipes open it takes 3 hours to fill the tank. How long w
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Question 232546: Pipe A can fill a tank in 5 hours. Pipe B can fill the tank in 2 hours less time than it takes pipe C to empty it. With all pipes open it takes 3 hours to fill the tank. How long will it take pipe C to empty the tank? Found 2 solutions by stanbon, ankor@dixie-net.com:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Pipe A can fill a tank in 5 hours. Pipe B can fill the tank in 2 hours less time than it takes pipe C to empty it. With all pipes open it takes 3 hours to fill the tank. How long will it take pipe C to empty the tank?
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Pipe A DATA:
filling rate = 1/5 tank/hr
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Pipe C DATA:
filling rate = 1/x tank/hr
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Pipe B DATA:
filling rate = 1/(x-2) tank/hr
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Together DATA:
filling rate = 1/3 tank/hr
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Equation:
rate + rate + rate = together rate
1/5 + 1/x + 1/(x-2) = 1/3
Multiply thru by 15x(x-2):
3x(x-2) + 15(x-2) + 15x = 5x(x-2)
etc.
I'll let you finish this.
Cheers,
Stan H.
You can put this solution on YOUR website! Pipe A can fill a tank in 5 hours. Pipe B can fill the tank in 2 hours less time than it takes pipe C to empty it. With all pipes open it takes 3 hours to fill the tank. How long will it take pipe C to empty the tank?
:
Let x = time required by pipe C to empty a full tank
then
(x-2) = time for Pipe B to fill the tank
:
Let the full tank = 1
;
Filling +, emptying -
:
Pipe A + Pipe B - Pipe C = a full tank + - = 1
:
Multiply equation by 5x(x-2), results
3x(x-2) + 5x(3) - 5(x-2)(3) = 5x(x-2)
;
3x^2 - 6x + 15x - 15(x-2) = 5x^2 - 10x
:
3x^2 - 6x + 15x - 15x + 30 = 5x^2 - 10x
:
3x^2 - 6x + 30 = 5x^2 - 10x
:
0 = 5x^2 - 3x^2 - 10x + 6x - 30
:
0 = 2x^2 - 4x - 30
:
Simplify divide by 2
x^2 - 2x - 15 = 0
:
Factors to:
(x-5)(x+3) = 0
Positive solution
x = 5 hrs, time pipe C needs to empty a full tank
then
5 - 2 = 3 hrs for pipe B to fill the tank
:
:
Since pipe A fills in 5 hrs and pipe C empties in 5 hrs we're left with pipe B which fills it in 3 hrs
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