$3-$ A highway connecting two small cities has the following characteristics: The time $($t$,$ min $)$ to travel on a certain stretch of a highway $($route $1)$ is t$\_1-12+0\mathrm{.}01$ q; where ql is the flow of vehicles$($veh$/$hr$).$ The demand function is q$=4800-100$ t$.$ Hint for Problem $3$: In this problem the total demand between two cities is given based on a function of time $($q$=4800-100$ t$).$ Therefore, whenever you need to find the demand function for all a$,$ b and c parts of question $3.$Citizens currently using the existing highway $($route $1)$ want to continue using it$,$ and, in addition, eager to have the new highway $($route $2)$ as well. What will be the equilibrium flow for routes $1$ and $2$ and travel time for this scenario, assuming the demand function for travel remains unchanged $($Wardrop$\text{'}$s principle applies$).$ Solve this problem based on User Equilibrium approach. $($Hint: For total demand between two cities, use the same demand function given before $)$