Chapter 3.3, Problem 62E

Traffic flow In the analyst of traffic flow, a certain city eatimates the following situation for the square of its downtown district. In the following figure, the arrows indicate the flow of traffic. If $x_1$ represents the number of cars traveling between intrsections $A$ and $B$, $x_2$ represents the number of cars traveling between $B$

and $C$, $x_3$ the number between $C$

and $D$, and $x_4$ 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

$200+x_4=100+x_1$

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

Solve the system of these four equations.

Can the entire traffic flow problem be studied and solved by counting only the $x_4$ cars that travel between $A$

and $D$

? Explain.

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