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Math Help - D.e mixing problem

  1. #1
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    D.e mixing problem

    300 gallon tank contains 100 gallons of brine with a concentration of 1 pound of salt per gallon.a brine containing one half point of salt per gallon runs into the tank at rate of four gallons per minute nad the well stirred mixture drains from the tank at the same rate .when is the concentration in the tank 0.7 pound per gallon .
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  2. #2
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    Let c be the concentration. Then c changes according to:

    \frac{dc}{dt}=\frac{\text{salt entering}-\text{salt leaving}}{100\text{ gallons}}

    The amount of salt entering the tank is \frac{1}{2}*4 pounds per minute.

    The amount of salt leaving the tank is c*4 pounds per minute.

    So you solve the differential equation and apply the initial condition c(0)=1 pound per gallon to evaluate the constant of integration, then set c(t)=0.7 and solve for t.

    Post again in this thread if you are still having trouble.

    - Hollywood
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