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Math Help - Pool filling word problem

  1. #1
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    Pool filling word problem

    There are 2 pipes. One is mainly used to fill up pool with water and another - to drain. It takes 2 hours more to fill up pool with water, than to drain. When we filled 1/3 of the pool with water, all 2 pipes were opened and the pool drained in 8 hours. How long does it take to fill up pool, when only 1 pipe is open?

    I've spent long time figuring this out, but never came close to answer - 8 hours.

    What the equation should look like? ;\

    Thanks.
    Last edited by Ellla; January 27th 2011 at 03:42 AM. Reason: Solved
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  2. #2
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    Quote Originally Posted by Ellla View Post
    There are 2 pipes. One is mainly used to fill up pool with water and another - to drain. It takes 2 hours more to fill up pool with water, than to drain. When we filled 1/3 of the pool with water, all 2 pipes were opened and the pool drained in 8 hours. How long does it take to fill up pool, when only 1 pipe is open?

    I've spent long time figuring this out, but never came close to answer - 8 hours.

    What the equation should look like? ;\

    Thanks.

    This problem belongs to prealgebra, not to calculus. Let x be the time in hours it takes pipe 2 to drain the pool, so

    that x+2 is the time it takes pipe 1 to fill it up, and from here \displaystyle{\frac{1}{x}\,,\,\frac{1}{x+2}} are the

    relative work done by pipe 2 draining (resp. pipe 1 filling) in 1 hour.

    When then we open up both pipes they drain the pool by a rate of \displaystyle{\frac{1}{x}-\frac{1}{x+2}=\frac{2}{x(x+2)}}-th of a pool every hour

    and we're said it takes then 8 hours to empty the pool, so we get:

    \displaystyle{\frac{1}{3}-8\cdot \frac{2}{x(x+2)}=0\Longrightarrow (x+8)(x-6)=x^2+2x-48=0\Longrightarrow x = 6 , as x must be

    positive, and thus indeed the time it takes to fill up the pool with pipe 1 alone is x+2=6+2=8 hours

    Tonio
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