Differential Equation Dilution problem

[Dluna08]

A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the well stirred mixture leaves the tank at the rate of 8 gal/min. a) set-up the DE to find an expression for the amount of salt in the tank after t min. b) find the amount of salt in the tank when the tank contains 40 gallons of solution

Homework Equations

when i set up my DE i end up with dQ/dt + 1/10Q = 4. I notice that this equation is linear with p(t) = 1/10. So I solve and get Q= 40 + ce^-t/10. I don't know how to find the amount of salt in the tank when the tank contains 40 gallons of solution??

The Attempt at a Solution

 

[lippyka]

a) dQ/dt + 1/10Q = 4b) Substituting Q=40, we get 0+1/10(40) = 4, which implies that c=4. Thus, the expression for the amount of salt in the tank after t min is: Q = 40 + 4e^-t/10.