# Mixture Problem (pls help)

#### johnglicer

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...

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

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