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A tank initially contains 50 gal of pure water. Brine containing 4 lb of salt per...

A tank initially contains 50 gal of pure water. Brine containing 4 lb of salt per gallon enters the tank at 2 ​gal/min, and the​ (perfectly mixed) solution leaves the tank at 3 ​gal/min. Thus, the tank is empty after exactly 50 min.

​(a) Find the amount of salt in the tank after t minutes.

​(b) What is the maximum amount of salt ever in the​ tank?

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