Two very large tanks A and B are each partially fi­lled with 100gallons of brine. Initially, 100 pounds of salt is dissolved in the solution in tank A and 50 pounds of salt is dissolved in thesolution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in the following figure.

(a) Use the information given in the fi­gure to construct a mathematical model for the number of pounds of salt x₁(t) and x₂(t) at time t in tanks A and B, respectively.

(b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. Explain why this relationship makes intuitive sense. Use this relationship to help fi­nd the amount of salt in tank B at t = 30 min.

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mixture 3 gal/min A 100 gal 100 gal mixture 2 gal/min