The accompanying figure shows the flow of traffic near a city's Civic Center during the rush hours on a typical weekday. Each road can handle a maximum of 1,000 cars/hour without causing congestion. The flow of traffic is controlled by traffic lights at each of the five intersections. Set up a system of linear equations describing the traffic flow and solve this system.
E) The system is inconsistent.

Question

The accompanying figure shows the flow of traffic near a city's Civic Center during the rush hours on a typical weekday. Each road can handle a maximum of 1,000 cars/hour without causing congestion. The flow of traffic is controlled by traffic lights at each of the five intersections.  Set up a system of linear equations describing the traffic flow and solve this system.
E) The system is inconsistent.

Quizplus · Accepted Answer

Let X1, X2, X3, X4, and X5 represent the number of cars per hour at each intersection. Then the system of equations is:

X2 + X4 = 1200
X1 + X2 = X5
X1 + X3 = 800
X3 + X4 = X5
X2 + X3 = 1000

Solving this system gives X1 = 200, X2 = 600, X3 = 400, X4 = 600, X5 = 800. These values satisfy all of the given constraints, so the answer is (B).

The Accompanying Figure Shows the Flow of Traffic near a City's