$(20$ points$)$ An origin$-$destination pair is connected by a route with a performance function $t_l=2+x_1^2,$ and another with a function $t_2=7+2x_2($with $x\text{'}$s in thousands of vehicles per hour and $t\text{'}$s in minutes$).$ If the total origin$-$destination flow is $5000ve\frac{h}{h},$ determine user equilibrium route travel time, total travel time $($in vehicle$-$minutes$),$ and route flows.