1. A large tank initially containing no salt and 200 gallons of water, has a solution of salt and
water with a concentration of 2 lbs per gallon of salt pumped in at a rate of 3 gallons per hour.
From another input pipe, pure water is pumped in at 1 gallon per hour. The (instantaneously,
perfectly mixed) solution drains from the tank at a rate of 4 gallons per hour.
(a) Set up and solve an IVP that models the amount of salt in the tank at time $t$. Solve this one
by hand and show your work.
(b) How does your IVP change if, instead of pure water, the tank starts with 200 gallons of a
solution with a concentration of 2 pounds per gallon of salt? (You don't have to solve again, just
give the new setup.)
