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. Solve the system of these four equations.

Question

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. Solve the system of these four equations.

Quizplus · Accepted Answer

We can formulate the equations for traffic at intersections B, C, and D using the principle that the number of vehicles entering an intersection equals the number leaving it. For intersection B: x₁ = xU2S1B22U2S1B0 + xU1S2B21U1S2B0 + xB13U1B23B1U1B0 For intersection C: x₂ = xU2S1B23U2S1B0 + xU1S2B32U1S2B0 + xB14U1B24B1U1B0 For intersection D: x₃ = xU2S1B24U2S1B0 + xU1S2B43U1S2B0 + xB11U1B21B1U1B0 We can substitute the given values into these equations and solve the resulting system of equations using Gaussian elimination or another method. Solving the system, we get: x₁ = 22 xU2S1B22U2S1B0 = 12 xU1S2B21U1S2B0 = 29 xB13U1B23B1U1B0 = 11 x₂ = 20 xU2S1B23U2S1B0 = 29 xU1S2B32U1S2B0 = 10 xB14U1B24B1U1B0 = 12 x₃ = 11 xU2S1B24U2S1B0 = 12 xU1S2B43U1S2B0 = 22 xB11U1B21B1U1B0 = 29 Therefore, the correct answer is choice B.

In the Analysis of Traffic Flow, a Certain City Estimates