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Homework Help: Differential Equation (mixture problem)

  1. Nov 4, 2006 #1
    A beer manufacturer needs to convert a tank containing 40 gallons of regular beer into light beer by adding water. Initially, water is pumped into the tank at the rate of 4 gal/min. And the perfectly mixed solution is allowed to flow out of the tank at the rate of 2 gal/min. The light beer has 1/3 calories of regular beer. That is, it is 2/3 water. How long will it take to convert the regular been into light beer?

    Can someone please help me set up and solve this problem. Im confused on what to use as the concentration of the solution.

    Formula: da/dt=R1-R2
    R1=(rate of substance entering)(concentration)
    R2=(rate of substacne leaving)(concentration)
    Last edited: Nov 4, 2006
  2. jcsd
  3. Nov 4, 2006 #2


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    I'm a bit confused by the question... it looks like they should just pump 80 gallons into the tank, then let it all out, because you can't (or can you?) start releasing perfectly mixed beer before you've added enough water to mix it all.
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