a tank contains 100 gal of freshwater. then water containing 0.5 lb of salt per gallon is poured into the tank at a rate of 3 gal/min , and the mixture is allowed to leave at the same rate. after 12 min the process is stopped, and fresh water is poured into the tank at a rate of 3 gal/min, with the mixture again leaving at the same rate. (a) solve the initial value problem valid for 0≤t≤12.