Traffic flow. In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If x₁ represents the number of cars traveling between intersections A and B, x2 represents the number of cars traveling between B and C, x3 the number between C and D, and x4 the number between D and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number leaving it. That is, for intersection A we obtain 200+x₁ = 100+x₁ Formulate equations for the traffic at B, C, and D. Solve the system of these four equations. Out 100 In 300 In 200 A x1 B Out 200 A 5 Out 800 D J x3 с In 200 In 500 Out 100
Traffic flow. In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If x₁ represents the number of cars traveling between intersections A and B, x2 represents the number of cars traveling between B and C, x3 the number between C and D, and x4 the number between D and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number leaving it. That is, for intersection A we obtain 200+x₁ = 100+x₁ Formulate equations for the traffic at B, C, and D. Solve the system of these four equations. Out 100 In 300 In 200 A x1 B Out 200 A 5 Out 800 D J x3 с In 200 In 500 Out 100
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:O x₁ = x₁ +100, x₂ = x4 +200, x3 = x4 +300, x4=X4
O x₁ = x4 +100, x₂ = x4 +300, x3 = x4 +100, x₁=X4
O x₁ = x₁ +100, x₂ = x4 +100, x3 = x4, X4=X4
O x₁ = x4 +100, x₂ = x4 +100, x3 = x4 +300, x₁=X4
O x₁ = x₁ +100, x₂ = x4 +200, x3 = x4 +100, x4 = X4
Transcribed Image Text:Traffic flow. In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district.
In the following figure, the arrows indicate the flow of traffic. If x₁ represents the number of cars traveling between intersections A
and B, x2 represents the number of cars traveling between B and C, x3 the number between C and D, and x4 the number between D
and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number
leaving it. That is, for intersection A we obtain
200+x4 = 100+x₁
Formulate equations for the traffic at B, C, and D. Solve the system of these four equations.
Out 100
In 300
200
A
X1
B
Out
200
34
Out
800
D
5
x2 C
In
200
In 500
Out 100
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