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Two pipes

  1. Feb 23, 2008 #1
    There are two pipes, Pipe A and Pipe B. Pipe A filled a tank in for minutes less than B does. If both pipes are open the tank is filled in 24 minutes. Find the time A will take if B is closed
     
  2. jcsd
  3. Feb 23, 2008 #2

    symbolipoint

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    The bulk of the analysis for a solution is to fill a chart for Rate, Time, Job, for each of pipe A, pipe B, and pipes A and B together. If anyone knows how to present a chart in the forum, please tell; anyway, I developed this information, using t as time for pipe B to fill the tank:

    pipe A: Rate? time=t-4 jobs=1
    pipe B: Rate? time=t jobs=1
    pipes A and B Together: Rate? time=24 minutes jobs=1

    That information further indicates that These rate expressions use:
    pipe A: Rate= 1/(t-4)
    pipe B: Rate= 1/t
    both pipes together: Rate=1/24

    I did not finish the solution. Can you continue from there?
     
  4. Feb 24, 2008 #3

    HallsofIvy

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    Or: add rates. Since the question asks how long it will take A to fill the tank alone, let that be T minutes. Then A's rate is 1/T "tanks per minute". Since A fills the tank in 4 minutes less than B, B fills the tank in 4 minutes longer than A: it fills the tank in T-4 minutes and so its rate is 1/(T-4) "tanks per minute". Together, their rate is 1/T+ 1/(T-4). We are told that the pipes can, together, fill the tank in 24 minutes: their rate together is 1/24 "tanks per minute". Since that is exactly what we calculated before,
    1/T+ 1/(T+ 4)=1/24. Solve that equation for T.
     
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