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Math Help - time......

  1. #1
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    Question time......

    Two taps 'a' and 'b' can fill a water tank in 9min and 12 min respectively.In what time it will be full, if 'b' starts working 2 min after 'a' starts working?...........
    Last edited by wonder; November 6th 2008 at 10:17 PM.
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  2. #2
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    Quote Originally Posted by wonder View Post
    Two taps 'a' and 'b' can fill a water tank in 9min and 12 min respectively.In what time it will be full, if 'b' starts working 2 min after 'a' starts working?...........
    Let T denote the volume of the tank.

    Then a delivers \dfrac T9 per minute and

    b delivers \dfrac T{12} per minute.

    After x minutes the tank is filled:

    \dfrac T9 \cdot x + \dfrac T{12} \cdot (x-2)=T . Divide by T, expand the brackets, collect like terms:

    \dfrac x9 + \dfrac x{12} - \dfrac16=1~\implies~\dfrac7{36} x=\dfrac76~\implies~\boxed{x=6}
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