Suppose a large tank can hold up to 600 gal of liquid. Initially it has 300 gal of water with 20lb of salt. A solution with 1/2 lb of salt per gallon is pumped into the tank at a rate of 5 gal/min, the solution is well mixed and being pumped out at the rate of 3 gal/min.
Let A(t) be the actual amount of salt in the tank at time t (in minutes).
Set up the initial value problem for A(t) and then determine the concentration of salt in the tank when it's full.
Solve using Linear differential equations.