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Math Help - Mixing problem, brine solution

  1. #1
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    Mixing problem, brine solution

    A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb of salt per gallon enters the tank at the rate of 4 gal/min, and the well mixed brine in the tank flows out at the rate of 3 gal/min. How much salt will the tank contain after 100 minutes?

    So, I get the integrating factor but then I'm lost.
    I(t)=(t+100)^3

    Thanks for any help.
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  2. #2
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    Re: Mixing problem, brine solution

    Quote Originally Posted by Lamont View Post
    A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb of salt per gallon enters the tank at the rate of 4 gal/min, and the well mixed brine in the tank flows out at the rate of 3 gal/min. How much salt will the tank contain after 100 minutes?

    So, I get the integrating factor but then I'm lost.
    I(t)=(t+100)^3

    Thanks for any help.
    What is your Differential Equation?
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  3. #3
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    Re: Mixing problem, brine solution

    I tried setting this up but I'm not sure if it's right.

    dy/dt = 4-3y/(100+t); y(0)=50
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  4. #4
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    Re: Mixing problem, brine solution

    Quote Originally Posted by Lamont View Post
    I tried setting this up but I'm not sure if it's right.

    dy/dt = 4-3y/(100+t); y(0)=50
    That's right.

    \frac{dy}{dt}+\frac{3y}{100+t}=4

    Integrating factor =\exp\left(\int \frac{3}{100+t}dt\right)=\exp[3\ln (100+t)]=(100+t)^3

    (100+t)^3\frac{dy}{dt}+3y(100+t)^2=4(100+t)^3

    \frac{d}{dt}[(100+t)^3y]=4(100+t)^3

    Can you proceed?
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  5. #5
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    Re: Mixing problem, brine solution

    Yeah, I think so. Thanks!
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