$(20$ points$)$ Based on the estimations of trip distribution and mode choice, there are $3000$ vehicle trips going from the Origin O to the Destination D$.$ Figure below shows the two routes and the cost $($travel time$)$ functions, where $V$ denotes volume and $T,$ travel time.

a$)$ Use the User Equilibrium $($UE$)$ method to determine the traffic assignment on two routes. Report the total travel times experienced by all travelers when the user equilibrium is reached.