A 150-galon tank initially contains 30 gal of pure water. Salt water solution containing 1.5 lb of salt per gallon begins entering the tank at a rate of 6 gal/min. Simul- taneously, a drain is opened at the bottom of the tank, allowing the well-stirred mixture to leave the tank at a rate of 3 gal/min. (a) Derive a differential equation that models the amount of salt in the tank after t minutes, for 0≤ t ≤ 40. You should also provide the appropriate initial value condition. (b) Solve the initial value problem derived in part (a). Find the amount of salt in the tank when it is half full.

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