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Math Help - Pipes and cistern problem. Pleae explain.

  1. #1
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    Pipes and cistern problem. Pleae explain.

    A and B can fill a cistern in 7.5 minutes and 5 minutes respectively and C can carry off 14 litres per minute. If the cistern is already full and all the three pipes are opened, then it is emptied in 1 hr. How may liters can it hold?
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    Re: Pipes and cistern problem. Pleae explain.

    Hey hisajesh.

    Can you show us any partial attempts you have tried on this problem? (Hint: It will involve derivatives).
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    Re: Pipes and cistern problem. Pleae explain.

    I took A and B as one pipe which fills 1/3 of the cistern every minute and you have a pipe C emptying 14 liters per minute. The cistern is already full in the begining.
    So I took the computation as 1+(1/3)(x)-14 litres=0
    so x=3.5 and the total cistern can have 10.5 liters.

    But the book answer is 40. Can you help?
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    Re: Pipes and cistern problem. Pleae explain.

    Quote Originally Posted by hisajesh View Post
    I took A and B as one pipe which fills 1/3 of the cistern every minute <-- that's correct
    and you have a pipe C emptying 14 liters per minute. The cistern is already full in the begining.
    So I took the computation as 1+(1/3)(x)-14 litres=0
    so x=3.5 and the total cistern can have 10.5 liters.

    But the book answer is 40. Can you help?
    1. Let V be the volume of the cistern.

    2. A and B add 1/3 of V to the filled cistern while C take 14 liters per minute from the cistern. After 1 h = 60 min the cistern is empty:

    V + (1/3) V* 60 - 14 * 60 = 0

    3. Solve for V.
    Thanks from hisajesh
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    Re: Pipes and cistern problem. Pleae explain.

    Pipes and cistern problem. Pleae explain.-cistern.png
    Quote Originally Posted by hisajesh View Post
    A and B can fill a cistern in 7.5 minutes and 5 minutes respectively and C can carry off 14 litres per minute. If the cistern is already full and all the three pipes are opened, then it is emptied in 1 hr. How may liters can it hold?
    Thanks from hisajesh
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