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 Formulate equations for the traffic at B, C, and D.

Question

Quizplus · Accepted Answer

For intersection B: x₁ + xS2U2B21S2U2B0 = x₂ + xS4U4B41S4U4B0 For intersection C: x₂ + xS3U3B31S3U3B0 = x₃ + xS2U2B21S2U2B0 For intersection D: x₃ + xS4U4B41S4U4B0 = x₄ + xS3U3B31S3U3B0 Option A is incorrect because it incorrectly adds x₃ twice to the equation for intersection D. Option B is incorrect because it is missing the x₂ term on the right-hand side of the equation for intersection C. Option D is incorrect because it adds x₁ twice to the equation for intersection B. Option E is incorrect because it is missing the xS4U4B41S4U4B0 term on the left-hand side of the equation for intersection D.

In the Analysis of Traffic Flow, a Certain City Estimates