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Math Help - Diff. Eq./Related rates

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    is up to his old tricks again! Jhevon's Avatar
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    Diff. Eq./Related rates

    Hey guys, can you help me with this problem?

    A tank initially contains 120 liters of pure water. A mixture containing a concentration of x g/liter of salt enters the tank at a rate of 2 liters/min, and the well-stirred mixture is allowed to leave the tank at the same rate. Find an expression in terms of x for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t-->infinity


    Thanks guys
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    Quote Originally Posted by Jhevon View Post
    Hey guys, can you help me with this problem?

    A tank initially contains 120 liters of pure water. A mixture containing a concentration of x g/liter of salt enters the tank at a rate of 2 liters/min, and the well-stirred mixture is allowed to leave the tank at the same rate. Find an expression in terms of x for the amount of salt in the tank at any time t. Also find the limiting amount of salt in the tank as t-->infinity


    Thanks guys
    Let Q(t) represent the amount of salt after t minutes.

    Then,
    dQ/dt = Rate in - Rate out

    The rate is is (x g/liter)*(2 liters/min) = 2x g/min.

    The rate out is (Concentration)*(2 liters/min)
    Now the concentration = Amount/Volume = Q/120
    Thus, rate out is (Q/120 g/liter)(2 liters/min)=Q/60 g/min.

    Thus, the differencial equation is,
    dQ/dt = 2x - Q/60
    Thus,
    dQ/dt + Q/60 = 2x
    With initial conditions Q(0)=0.

    This is a first order linear differencial equation, it solves easily. I am sure you can do it from there.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Yes, I can take it from there, thanks.
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