Two tanks are interconnected. Tank A contains 70 grams of salt in 40 liters of water, and Tank B contains 60 grams of salt in 50 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 10 L/min, while a solution of 5 grams/L flows into Tank B at a rate of 5 L/min. The tanks are well mixed. The tanks are connected, so 11 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
Two tanks are interconnected. Tank A contains 70 grams of salt in 40 liters of water, and Tank B contains 60 grams of salt in 50 liters of water. A solution of 1 gram/L flows into Tank A at a rate of 10 L/min, while a solution of 5 grams/L flows into Tank B at a rate of 5 L/min. The tanks are well mixed. The tanks are connected, so 11 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
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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Transcribed Image Text:Two tanks are interconnected. Tank A contains 70 grams of salt in 40 liters of water, and Tank B contains 60
grams of salt in 50 liters of water.
A solution of 1 gram/L flows into Tank A at a rate of 10 L/min, while a solution of 5 grams/L flows into
Tank B at a rate of 5 L/min. The tanks are well mixed.
The tanks are connected, so 11 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to
Tank A. An additional 15 L/min drains from Tank B.
Letting a represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the
system of differential equations for these two tanks.
=10-7x+
dz
dt
dy
dt
6
= 25+y-x-18y
r(0) =
, y(0) =
X
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