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We have a system of two interconnected tanks initially with Tank A holding 22 gal of water and 10 oz of salt, and Tank B holding 17 gal of water and 12 oz of salt. A brine with salt concentration 8 oz/gal flows into Tank A at a rate of 5 gal/min, and the solution in Tank A is discharged from the system at a rate of 2 gal/min. A brine with salt concentration 3 oz/gal flows into Tank B at a rate of 6 gal/min, and the solution in Tank B is discharged from the system at a rate of 9 gal/min. The two tanks are interconnected by two pipes: through one of the pipes the solution flows from Tank A to Tank B at a rate of 7 gal/min, and through the other pipe the solution flows from Tank B to Tank A at a rate of 4 gal/min. Denote by Q1(t) and Q2 (t) respectively, the amounts of salt in Tanks A and B after t minutes. Write the initial value problem for Q1(t) and Q2 (t); that is, write the differential equations and the initial conditions for Q1 (t) and Q2 (t).

We have a system of two interconnected tanks initially with Tank A holding 22 gal of water and 10 oz of salt, and Tank B holding 17 gal of water and 12 oz of salt. A brine with salt concentration 8 oz/gal flows into Tank A at a rate of 5 gal/min, and the solution in Tank A is discharged from the system at a rate of 2 gal/min. A brine with salt concentration 3 oz/gal flows into Tank B at a rate of 6 gal/min, and the solution in Tank B is discharged from the system at a rate of 9 gal/min. The two tanks are interconnected by two pipes: through one of the pipes the solution flows from Tank A to Tank B at a rate of 7 gal/min, and through the other pipe the solution flows from Tank B to Tank A at a rate of 4 gal/min. Denote by Q1(t) and Q2 (t) respectively, the amounts of salt in Tanks A and B after t minutes. Write the initial value problem for Q1(t) and Q2 (t); that is, write the differential equations and the initial conditions for Q1 (t) and Q2 (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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We have a system of two interconnected tanks initially with Tank A holding 22 gal of water and 10 oz of salt, and Tank B holding 17 gal of water and 12 oz of salt. A brine with salt concentration 8 oz/gal flows into Tank A at a rate of 5 gal/min, and the solution in Tank A is discharged from the system at a rate of 2 gal/min. A brine with salt concentration 3 oz/gal flows into Tank B at a rate of 6 gal/min, and the solution in Tank B is discharged from the system at a rate of 9 gal/min. The two tanks are interconnected by two pipes: through one of the pipes the solution flows from Tank A to Tank B at a rate of 7 gal/min, and through the other pipe the solution flows from Tank B to Tank A at a rate of 4 gal/min. Denote by Q1(t) and Q2 (t) respectively, the amounts of salt in Tanks A and B after t minutes. Write the initial value problem for Q1 (t) and Q2(t); that is, write the differential equations and the initial conditions for Q1 (t) and Q2 (t). Remark 1: You need to show the derivation of the differential equations. Remark 2: You are NOT required to solve Q1 (t) and Q2 (t).
Transcribed Image Text:We have a system of two interconnected tanks initially with Tank A holding 22 gal of water and 10 oz of salt, and Tank B holding 17 gal of water and 12 oz of salt. A brine with salt concentration 8 oz/gal flows into Tank A at a rate of 5 gal/min, and the solution in Tank A is discharged from the system at a rate of 2 gal/min. A brine with salt concentration 3 oz/gal flows into Tank B at a rate of 6 gal/min, and the solution in Tank B is discharged from the system at a rate of 9 gal/min. The two tanks are interconnected by two pipes: through one of the pipes the solution flows from Tank A to Tank B at a rate of 7 gal/min, and through the other pipe the solution flows from Tank B to Tank A at a rate of 4 gal/min. Denote by Q1(t) and Q2 (t) respectively, the amounts of salt in Tanks A and B after t minutes. Write the initial value problem for Q1 (t) and Q2(t); that is, write the differential equations and the initial conditions for Q1 (t) and Q2 (t). Remark 1: You need to show the derivation of the differential equations. Remark 2: You are NOT required to solve Q1 (t) and Q2 (t).
We have a system of two interconnected tanks initially with Tank A holding 22 gal of water and 10 oz of salt, and Tank B holding 17 gal of water and 12 oz of salt. A brine with salt concentration 8 oz/gal flows into Tank A at a rate of 5 gal/min, and the solution in Tank A is discharged from the system at a rate of 2 gal/min. A brine with salt concentration 3 oz/gal flows into Tank B at a rate of 6 gal/min, and the solution in Tank B is discharged from the system at a rate of 9 gal/min. The two tanks are interconnected by two pipes: through one of the pipes the solution flows from Tank A to Tank B at a rate of 7 gal/min, and through the other pipe the solution flows from Tank B to Tank A at a rate of 4 gal/min. Denote by Q1(t) and Q2 (t) respectively, the amounts of salt in Tanks A and B after t minutes. Write the initial value problem for Q1 (t) and Q2(t); that is, write the differential equations and the initial conditions for Q1 (t) and Q2 (t). Remark 1: You need to show the derivation of the differential equations. Remark 2: You are NOT required to solve Q1 (t) and Q2 (t).
Transcribed Image Text:We have a system of two interconnected tanks initially with Tank A holding 22 gal of water and 10 oz of salt, and Tank B holding 17 gal of water and 12 oz of salt. A brine with salt concentration 8 oz/gal flows into Tank A at a rate of 5 gal/min, and the solution in Tank A is discharged from the system at a rate of 2 gal/min. A brine with salt concentration 3 oz/gal flows into Tank B at a rate of 6 gal/min, and the solution in Tank B is discharged from the system at a rate of 9 gal/min. The two tanks are interconnected by two pipes: through one of the pipes the solution flows from Tank A to Tank B at a rate of 7 gal/min, and through the other pipe the solution flows from Tank B to Tank A at a rate of 4 gal/min. Denote by Q1(t) and Q2 (t) respectively, the amounts of salt in Tanks A and B after t minutes. Write the initial value problem for Q1 (t) and Q2(t); that is, write the differential equations and the initial conditions for Q1 (t) and Q2 (t). Remark 1: You need to show the derivation of the differential equations. Remark 2: You are NOT required to solve Q1 (t) and Q2 (t).
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