$(20$ points$)$ Vehicles begin to arrive at a park entrance at $7$:$45am$ at a constant rate of $6$ per

minute and at a constant rate of $4$ vehicles per minute from $8$:$00$am on$.$ The park opens at

$8$:$00$am and the manager wants to set the departure rate so that the average delay per vehicle

is no greater than $9$ minutes $($measured from the time of the first arrival until the total queue

clears$).$ What is the minimum departure rate needed to achieve this? $($assume $\frac{D}{D}\frac{?}{1})$