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Homework Help: Differential Equations mixing sugar and water

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data

    A tank contains 2860 L of pure water. A solution that contains 0.04 kg of sugar per liter enters a tank at the rate 5 L/min The solution is mixed and drains from the tank at the same rate. Find the amount of sugar in the tank after t minutes.

    2. Relevant equations

    3. The attempt at a solution

    Obviously it starts with 0 kg sugar and an initial condition at time t = 0.
    The rate then would be equal to (the rate entering) - (the concentration exiting).
    Entering = .04*5 = .2
    Exiting = (Y*5)/2860 = Y/572

    dY/dt = .2 - Y/527
    dY/(.2 - Y/572) = dt
    integrate both sides
    -572ln(.2-Y/572) = t + C
    ln(.2 - Y/572) = -t/572 + C
    .2 - Y/572 = e^(-t/572+C)
    -Y/572 = Ce^(-t/572) - .2
    Y = Ce^(-t/572) + 114.4
    initial value t = 0 and Y = 0
    0 = Ce^(-0/572) + 114.4
    C = -114.4
    so Y = 114.4 - 114.4e^(-t/572)

    Is this right because I've done it a bunch of times and keep getting the same answer, but it's an online problem and it tells me that it's wrong and I can't figure out what I did incorrectly. Thanks!
  2. jcsd
  3. Sep 23, 2010 #2


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    Science Advisor
    Homework Helper

    I don't see anything wrong with your solution. Beats me why the online thing won't take it.
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