Traffic Flow

Traffic engineers use systems of equations to study the flow of traffic. The analysis of traffic flow is based on the principle that the number of cars that enter and leave an intersection must be equal. Suppose the traffic flow for some one-way streets can be modeled by the diagram below, where the numbers and the variables represent the numbers of cars entering or leaving an intersection per hour.

Letx1,x2, andx3represent the number of cars per hour that are traveling onAC,AB, andBC, respectively. Consider intersectionA. There are300 + 200 = 500cars per hour enteringAandx1+ x2cars leavingA. Therefore,x1+ x2= 500.For intersectionB, we have50 + x2cars per hour entering the intersection and100 + x3cars leaving the intersection. Thus50 + x2= 100 + x3, orx2- x3= 50. Applying the same reasoning toC, we havex1+ x3= 450. These equations result in the system of equations:

Using this example, estimate the traffic flow for a roundabout presented below. The graphical model shows the number of cars per hour that are entering or leaving a roundabout. If the portion of the roundabout betweenAandBhas an estimated traffic flow of from 66to 82cars per hour, what is the estimated traffic flow betweenCandA,and betweenBandC?

Work this custom problem about the systems of linear equations and solving linear inequalities using the techniques you learned in this module.