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Math Help - [SOLVED] Application Differential Equation: mixture problem.

  1. #1
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    [SOLVED] Application Differential Equation: mixture problem.

    An aquarium pool has volume 2 10^6 liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 10 grams/liter of salt is poured into the pool at a rate of 60 liters/minute. The salt water instantly mixes with the fresh water, and the excess mixture is drained out of the pool at the same rate (60 liters/minute).

    I need to figure out how to "Write a differential equation for S(t), the mass of salt in the pool at time t."


    Any help is appreciated.
    Last edited by Latszer; April 26th 2010 at 01:30 PM.
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  2. #2
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    Quote Originally Posted by Latszer View Post
    An aquarium pool has volume 2 106 liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 10 grams/liter of salt is poured into the pool at a rate of 60 liters/minute. The salt water instantly mixes with the fresh water, and the excess mixture is drained out of the pool at the same rate (60 liters/minute).

    I need to figure out how to "Write a differential equation for S(t), the mass of salt in the pool at time t."


    Any help is appreciated.
    Rate of salt in = (10)(60) = 600 gram/min.

    Rate of salt out = (C)(60) = (S/212)(60) = 15S/53 gram/min,

    where C is the concentration of salt in the tank at time t.

    Therefore ....
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  3. #3
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    dS/dt should be in-out so...

    600-3S/100000

    EDIT: ok nm...that was 10^6 not 106.

    Sorry about posting in calculus, I am still in calculus II and forgot I should post this in the DE section (we are doing DE for the last two weeks of class).
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  4. #4
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    I got the equation S(t) to be S = Aexp(3t/100000), if the pool is fresh initially would A jsut be 1?
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  5. #5
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    I got it...

    The final answer was S(t)=-20000000exp((-3t)/100000)+20000000

    Thanks for the help
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