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Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are 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 the figure below. dx1 dt dx2 dt x₁ (0) = A 100 gal (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. x₂(0) = mixture 3 gal/min mixture 2 gal/min lbs B 100 gal lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₂ for x₂(t).)

Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are 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 the figure below. dx1 dt dx2 dt x₁ (0) = A 100 gal (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. x₂(0) = mixture 3 gal/min mixture 2 gal/min lbs B 100 gal lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₂ for x₂(t).)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are 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 the figure below. dx₁ dt dx2 dt (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. = x₂(0) || x₁ (0) = A 100 gal = mixture 3 gal/min mixture 2 gal/min lbs B 100 gal lbs lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₁ for x₂(t).) Explain why this relationship makes intuitive sense. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, salt enters the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t = 25 min. (Round your answer to one decimal place.) X₂(25) =
Transcribed Image Text:Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105 pounds of salt are dissolved in the solution in tank A and 45 pounds of salt are 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 the figure below. dx₁ dt dx2 dt (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. = x₂(0) || x₁ (0) = A 100 gal = mixture 3 gal/min mixture 2 gal/min lbs B 100 gal lbs lbs (b) Find a relationship between the variables x₁(t) and x₂(t) that holds at time t. (Write an equation using x₁ for x₁(t) and x₁ for x₂(t).) Explain why this relationship makes intuitive sense. Since the system is closed, no salt enters or leaves the system. Since the system is closed, salt is not exchanged between the two tanks. Since the system is closed, salt enters and leaves the system at the same rate. Since the system is closed, salt leaves the system at a constant rate. Since the system is closed, salt enters the system at a constant rate. Use this relationship to help find the amount of salt in tank B at t = 25 min. (Round your answer to one decimal place.) X₂(25) =
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