Route Choice The cost of roadway improvements to the developer is a function of the amount of traffic being generated by the theater as well as the routes that these vehicles use in getting to/from the theater. Thus, you need to determine traffic demand on the available routes between the housing area (apartment complexes) and the proposed theater site. There are two potential routes from this housing area to the proposed theater site. The total flow on these two routes (origin-to-destination demand plus other traffic) is 5500 vehicles. These routes have the following speed and length characteristics: Route Free Flow Speed(mi/h) Length(mi)
1 45 5.5
2 40 3.5
3 35 3.75

It is known that the individual route travel times increase (in units of minutes) according to the following functions (with x in units of 1000 vehicles per hour):

Route Travel time increase as a function of traffic volume
1 0.5x1
2 x2
3 0.25

Required:
Determine user equilibrium flows and travel times if the total flow on these routes (origin-to-destination demand plus other traffic) is 5500 veh/h.