Tanks T(1) and T (2) contain 75 gallons and 125 gallons of salt solutions, respectively. A solution with 3 pounds of salt per gallon is pumped into T(1)from an external source at 1 gal/min, and a solution with 4 pounds of salt per gallon is pumped into T(2) from an external source at 2 gal/min. The solution from T(1) is pumped into T (2) at 3 gal/min, and the solution from T(2) is pumped into T(1) at 4 gal/min. T(1) is drained at 2 gal/min and T(2) is drained at 1 gal/min. Let Q 1 (t) and Q 2 (t) be the number of pounds of salt in T(1)and T(2), respectively, at time t> 0. Derive a system of differential equations for Q(1) and Q(2). Assume that both mixtures are well stirred. No need to solve the system.

Tanks T(1) and T (2) contain 75 gallons and 125 gallons of salt solutions, respectively. A solution with 3 pounds of salt per gallon is pumped into T(1)from an external source at 1 gal/min, and a solution with 4 pounds of salt per gallon is pumped into T(2) from an external source at 2 gal/min. The solution from T(1) is pumped into T (2) at 3 gal/min, and the solution from T(2) is pumped into T(1) at 4 gal/min. T(1) is drained at 2 gal/min and T(2) is drained at 1 gal/min. Let Q 1 (t) and Q 2 (t) be the number of pounds of salt in T(1)and T(2), respectively, at time t> 0. Derive a system of differential equations for Q(1) and Q(2). Assume that both mixtures are well stirred. No need to solve the system.

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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Question

100%

Tanks T(1) and T (2) contain 75 gallons and 125 gallons of salt solutions, respectively. A solution with
3 pounds of salt per gallon is pumped into T(1)from an external source at 1 gal/min, and a solution with
4 pounds of salt per gallon is pumped into T(2) from an external source at 2 gal/min. The solution from
T(1) is pumped into T (2) at 3 gal/min, and the solution from T(2) is pumped into T(1) at 4 gal/min. T(1)
is drained at 2 gal/min and T(2) is drained at 1 gal/min. Let Q 1 (t) and Q 2 (t) be the number of pounds
of salt in T(1)and T(2), respectively, at time t > 0. Derive a system of differential equations for Q(1) and
Q(2). Assume that both mixtures are well stirred. No need to solve the system.

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