A tank with a maximum capacity of 200 L contains salt water and is initially half full. The 100 L of salt water initially in the tank contains 20 kg of salt. A salt water solution with kg/L is added to the tank at a rate of 4 L/min and the liquid in the tank is drained at 2 L/min. You may assume the salt water solution in the tank is well-mixed at all times. (You may restrict your solution until the time that the tank fills up.) (a) What is the volume V (t) of liquid (in L) in the tank at time / (in minutes). (b) Write out an initial value problem describing the amount of salt y(1) (in kg) in the tank at time 1. (c) Solve your initial value problem for y(1). (d) At the moment in time when the tank fills to capacity, what amount of salt is in the t tank?