1. [ 20 points] An open tank with a capacity of 500 gal originally contains 200 gal of water in which 100lb of salt is dissolved. Four gal/min of a salt solution containing 2.5lb salt per gallon enters the tank from the top, and the mixture is allowed to flow out of the tank at a rate of two (2) gal/min from the bottom. Find: a). [5 points] the volume of solution in the tank at any time, t, prior ta the instant when the solution begins to overflow assuming the densities of all solutions are the same. b). [15 points] the amount of salt in the tank at any time, t, prior to the instant when the solution begins to overflow. Indicate the time range for which your solution is valid