Question $6(20$ points$)$: An incident occurs on a freeway that has a capacity of $3800$ veh$/$h and a constant flow rate of $3000ve\frac{h}{h}.$ At $7$:$35$ AM and an incident occurs that closes the freeway. At $7$:$55$ AM the freeway is partially opened with a flow rate of $1800vph.$ Finally, at $8$:$15$ AM the wreckage is removed, and the freeway resumes operating at the capacity. Determine the total delay $($in units of veh$-$min$)$ from the moment the incident occurs to the moment the queue is