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Mixture Problem (pls help)

  1. Mar 14, 2009 #1
    1. The problem statement, all variables and given/known data
    A tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal of salt
    enters at 2 gal/min, and the solution exits at 2 lb/gal. Find the amount of salt in the
    tank at any time...

    R1=C1Q1(c=concentration q=liquid substance or water ) this is the entering state
    C1=2 lb/gal
    Q1= 2gal/min

    R2=C2Q2(same as above but) this is the exit state
    C2= 2lb/gal
    Q2= unknown

    v= 80gallons


    2. Relevant equations

    dx/dt = R1 - R2
    dx/dt = C1*Q1 - C2*Q2

    but C2= x / vf
    vf= v+ (Q1-Q2)t


    3. The attempt at a solution
    I tried to "alterate the formula or relevant equation given

    of C2= x/vf to Q2= x/vf since i cant figure it out
    then vf= 80+(2-0)t ;since q2 is not given(is this proper?)
    vf=80+t
    then
    C2= x/(80+t)
    dx/dt = R1 - R2
    dx/dt = C1*Q1 - C2*Q2
    dx/dt= 2(2) - 2x/(80+t)
    dx/dt = 4 - 2x/(80+t) ;this is were I stuck up;; thought that it was separable

    but I knew from the start that altering the equation is completely insane,, please help me out guys,,, if only C2 is not given then Q2 shows,, this would be easy...

    please help me guys!


    An image is provided just in case to sum it up..
     

    Attached Files:

  2. jcsd
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