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#1 Re: Help Me ! » DiffEq Mixing Problems » 2012-10-08 13:02:35

Thankyou very much to both of you!

#2 Help Me ! » DiffEq Mixing Problems » 2012-10-07 11:58:37

Eileen
Replies: 4

I am having difficulty getting the correct answers to two mixing problems. If anyone would kindly help me out, it'd be much appreciated!

Problem1:
A tank initially holds 25 gal of water. Salt enters at a rate of 2gal/min and the mixture leaves at a rate of 1 gal/min. What will be the concentration of salt when 50 gal of fluid is in the tank?
   dA/dt=2-[A(t)/(t+25)]
   IF=(t+25)
   A(t+25)=(t^2)+50t+c
   A=[(t^2)+50t+c]/(t+25)
   For A(0)=0; c=0
   A=[(t^2)+50t]/(t+25)
   50=[(t^2)+50t]/(t+25)
   t=35.36
   35.36/50=.71

       The answer should be 75%.


Problem 2:
A tank initially contains 100 gal of a solution that holds 30lb of a chemical. A solution containing 2 lb/gal of the chemical runs in at a constant rate and the mixture runs out at the same rate. What should be the rate of flow if the tank is to contain 70lb of the chemical after 40min?
   dA/dt=2r-(A(t)*r/100)
   A(t)=ce^(-rt/100)+200
   70=ce^(-40r/100)+200
   -130=ce^(-2r/5)
   ln(-130)=ln(c)*ln(e^-2r/5)
   ln(-130)=c*2r/5
   (5/2)ln(-130)=r

       The answer should be (5/2)ln(17/13)=.671

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