Two very large tanks A and B are each partially fi shy lled 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 fi shy gure to construct a mathematical model for the number of pounds of salt x 1 (t) and x 2 (t) at time t in tanks A and B, respectively (b) Find a relationship between the variables x 1 (t) and x 2 (t) that holds at time t Explain why this relationship makes intuitive sense Use this relationship to help fi shy nd the amount of salt in tank B at t 30 min mixture 3 gal min A 100 gal 100 gal mixture 2 gal min

Question: 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

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.

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

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