Two routes connect an origin-destination pair with performance functions

1. t_1 = 5 + (x_1/2)^2

2. t_2 = 7 + (x_2/4)^2

(with t in minutes and x in thousands of vehicles per hour).

it is known that at user equilibrium, 75% of the origin-destination demand takes the first route.

what percentage would take the first route if a system-optimal solution were achieved and how much total travel time would be saved?

Air inially occupying a volume of 1 m2 at 100 kpa, 27 c undergoes three internally reversible processes in series. process 1-2 compression to 500 kpa during which pv constant process 2-3 adiabatic expanslon to 100 kpa process 3-1: constant-pressure expansion to 100 kpa (a) calculate the change of entropy for each of the three processes. (b) calculate the heat and work involved in each process. (c) is this cycle a power cycle or refrigeration cycle?