Two very large tanks A and B are each partially filled with 100 gallons of brine. Initia...

Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100 pounds of salt is dissolved in the solution in tank A and 50 pounds of salt is dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in Figure 3.3.6.

(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.