A tank initially contains 50 gal of pure water. Brine containing 3 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? 3 (a) The amount of salt x in the tank after t minutes is x = 3(50-t) - 2500 (b) The maximum amount of salt in the tank was about lb. (Type an integer or decimal rounded to two decimal places as needed.) -t)³ (50 -

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A tank initially contains 50 gal of pure water. Brine containing 3 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?
3
(a) The amount of salt x in the tank after t minutes is x = 3(50-t) -
2500
(b) The maximum amount of salt in the tank was about lb.
(Type an integer or decimal rounded to two decimal places as needed.)
(50 – t) ³
Transcribed Image Text:A tank initially contains 50 gal of pure water. Brine containing 3 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? 3 (a) The amount of salt x in the tank after t minutes is x = 3(50-t) - 2500 (b) The maximum amount of salt in the tank was about lb. (Type an integer or decimal rounded to two decimal places as needed.) (50 – t) ³
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