Problem 9:

A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Find the quantity Q.t/ of salt in the tank at time t > 0.

Problem 11:

A 200 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

Problem 15:

TankT1 initially contains 50 gallons of pure water. Starting at t0 D 0, water that contains 1 pound of salt per gallon is poured into T1 at the rate of 2 gal/min. The mixture is drained from T1 at the same rate into a second tank T2, which initially contains 50 gallons of pure water. Also starting at t0 D 0, a mixture from another source that contains 2 pounds of salt per gallon is poured into T2 at the rate of 2 gal/min. The mixture is drained from T2 at the rate of 4 gal/min. (a) Find a differential equation for the quantity Q.t/ of salt in tank T2 at time t > 0. (b) Solve the equation derived in (a) to determine Q.t/. (c) Find limt!1Q.t/.