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Math Help - pipes and cistern problem.

  1. #1
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    pipes and cistern problem.

    Pipes A and B can fill a cistern in 20 and 30 minutes and C can empty it in 15 minutes.
    If the three are opened and closed one after the other successively for 1 min each in that order, how soon will the cistern be filled?

    My answer is 180 min but the books answer is 167 minutes, kindly help.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: pipes and cistern problem.

    I would look at one 3 minute cycle:

    minute 1: A is open, B is closed, C is closed. Thus 1/20 of the cistern is filled.

    minute 2: A is closed, B is open, C is closed. Thus 1/30 of the cistern is filled.

    minute 3: A is closed, B is closed, C is open. Thus 1/15 of the cistern is drained.

    During this cycle, we have a net increase of 1/20 + 1/30 - 1/15 = 1/60

    After the 55th cycle we have 11/12 of the cistern filled, so we only need an additional 2 minutes of the next cycle to fill it for a total of 167 minutes.
    Last edited by MarkFL; December 13th 2012 at 09:37 PM.
    Thanks from hisajesh
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  3. #3
    MHF Contributor MarkFL's Avatar
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    Re: pipes and cistern problem.

    I wanted to post to let you know I was also tricked by the problem at first, and revised my reply above.
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    Re: pipes and cistern problem.

    Wow, got it! Thanks again!
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: pipes and cistern problem.

    Whew! I was afraid you had left, thinking the book was wrong! I apologize and I am glad you came back to see the correct reasoning!
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  6. #6
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    Re: pipes and cistern problem.

    I was relieved that someone supported my answer but super excited to understand the trick, math and nature are great!
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