Problem 2: An urban expressway, 8 miles long with three lanes for each direction of flow, is used by autos and buses. During the peak hour, an approximate service function for this facility IS: Where: t is travel time in minutes per mile, k is the number of lanes per direction, (:1G I 1200 automobiles per hour per lane, q is the total one way ow in automobiles per hour, 111 = 3 minutes per mile, and to = 1.2 minutes per mile. One bus is considered equivalent to 1.6 automobiles and the ow stream in the peak hour includes 30 buses With 40 passengers maximum capacity each. The demand functions for auto and bus usage in the corridor have been estimated to be: V, = V} a,tA +b,t, V, = V; +a,r, 4::er Where VA, VB are the numbers of auto and bus passengers per hour, and tA, tB are the total travel times (in minutes) for the expressway by auto and bus respectively. We Will assume a single passenger (the driver) for each automobile and VA0 = 2575, V30 = 1225, a1 = 40, a2 = 35, b1: 65, b; = 50. Assume also no intermediate stops for the buses and no congestion at entrance or exit ramps. 1. What are the total travel times for buses and automobiles over the expressway? What are the number of autos using the facility and the average number of passengers in each bus