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Homework Help: Calculus 2- Differential Equation Mixing Problem

  1. Jun 17, 2013 #1
    1. The problem statement, all variables and given/known data
    A tank containing 400 liters of water has 10 kg of salt solute (dissolved salt).
    Some brine containing 0.03kg/L of salt is then introduced at a rate of 2 L/min.
    The solution is constantly mixed and evacuated at a rate of 2L/min, such that the volume remains constant.

    If Q(t) is defined as the quantity of salt (in kg) dissolved in the tank after time t (in minutes),

    How do you find the differential equation?

    2. Relevant equations

    dQ/dt = Rin-Rout

    3. The attempt at a solution

    I have no idea how to find Rin or Rout, what do you need in their equations?
  2. jcsd
  3. Jun 17, 2013 #2
    Surely you know how much salt is being added! That information is given to you directly.

    If Q(t) is the amount of salt in the tank, the volume of the solution is 400 L and the rate at which the solution is being removed is 2 L/min, then how much salt is being removed every minute?
  4. Jun 17, 2013 #3
    Rin is added and Rout is removed right?

    ummmm 0.03kg/l, so 0.06 kg of salt is being removed every minute?

    0.03kg/l introduced at 2l/min isnt it also 0.06 being introduced? or do i have to add 10kg of solute with it?

    I am confused with these kind of word problems and my english is bad.
  5. Jun 17, 2013 #4
    How can you know how much salt is being removed, without knowing how much salt there is?
  6. Jun 17, 2013 #5


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    writing equations involving unknown quantities is the whole point of algebra, isn't it?

    Q(t) is the amount of salt in the tank so Q(t)/400 is the amount of salt per Liter. Since the volume remains constant, brine is going out at 2 L/min, the same rate it is coming in, and that means 2(Q(t)/400)= Q(t)/200. dQ/dt represents the change in Q and there are two kinds of change: salt coming in will be positive, salt going out will be negative.
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