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 3.3.7.(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. FIGURE 3.3.7 Mixing tanks in Problem 9Chapter 3.3, Problem 9E, Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100
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 3.3.7.
(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.
FIGURE 3.3.7 Mixing tanks in Problem 9
Chapter 3.3, Problem 9E, Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100
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