12. Mixing problem 1. A tank contains 100 L of water. A solution with salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. (a) If y(t) is the amount of salt (in kg) after t minutes, show that y satisfied the ODE: dy dt 3y 100+2t (b) Solve the above ODE, and find the concentration after 20 minutes. (3)