Chapter 2.3, Problem 4P

A tank with a capacity of $500\text{gal}$ originally contains $200\text{gal}$ of water with $100\text{lb}$ of salt in solution. Water containing $1\text{lb}$ of salt per gallon is entering at a rate of $3\text{gal}/\min$, and the mixture is allowed to flow out of the tank at a rate of $2\text{gal}/\min$. Find the amount of salt in the tank at any time prior to the instant when the solution begins to overflow. Find the concentration (in pounds per gallon) of salt in the tank when it is on the point of overflowing. Compare this concentration with the theoretical limiting concentration if the tank had infinite capacity.