Tank 1 initially contains 100 gallons of brine with 10 lb of salt dissolved in it and Tank 2 contains 50 gallons of pure water. Pure water flows from an outside source into Tank 1 at 5 gal/min. The mixture flows from Tank 1 into Tank 2 at the same rate and, with the same rate, it is discharged out of the system from Tank 2. Assume that solutions are well-stirred in each tank. Denoted by x 1(t) and x2(t), the amounts of salt in the two tanks after t minutes. Required:
a. Write the initial value problem for x1(t) and x2(t).
b. Find x1(t) and x2(t).
c. Find the maximum amount of salt ever in Tank 2.