A200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. a salt solution with 1/4 pound of salt per gallon is added to the tank at 4 gal/min, and the resulting mixture is drained out at 2 gal/min. find the quantity of salt in the tank as it’s about to overflow.

The volume of the solution in the tank is



and so the solution will overflow when . This happens at .

Now the rate of change of the amount of salt in the tank at time , , is described by




which is linear in . Multiplying both sides by , we have






There are 20 lbs of salt in the tank at the start, so and we get that



so that the amount of salt in the tank is given by the function



At , the tank contains



pounds of salt.