Two 100-gallon tanks initially contain pure water. Brine containing 2 lb of salt per gallon enters the first tank at the rate of 1 gal/min, and then the mixed solution drains into the second tank at the same rate. There, it is again thoroughly mixed and drains at the same rate, 1 gal/min.
Let S(t)=S(1)-S(2). Intuitively, S(t)>=0 for all t. At what time is the excess S(t) maximized? What is the maximum excess?