University of Phoenix Material
Figure 1 shows the intersections of five one-way streets and the number of cars that enter each intersection from both directions. For example, I1 shows that 400 cars per hour enter from the top and that 450 cars per hour enter from the left. See the Applications section in Section 6.2 of College Algebra as a reference.
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Figure 1. The intersections of five one-way streets
The letters a, b, c, d, e, f, and g represent the number of cars moving between the intersections. To keep the traffic moving smoothly, the number of cars entering the intersection per hour must equal the number of cars leaving per hour.
1. Describe the situation.
2. Create a system of linear equations using a, b, c, d, e, f, and g that models continually flowing traffic.
3. Solve the system of equations. Variables f and g should turn out to be independent.
4. Answer the following questions:
a. List acceptable traffic flows for two different values of the independent variables.
b. The traffic flow on Maple Street between I5 and I6 must be greater than what value to keep traffic moving?
c. If g = 100, what is the maximum value for f?
d. If g = 100, the flows represented by b, c, and d must be greater than what values? In this situation, what are the minimum values for a and e?
e. This model has five one-way streets. What would happen if the model had five two-way streets?