Question

$5\mathrm{.}22$ Vehicles begin to arrive at a

toll booth at $7$:$50$ A $.$ M $.$ with an

arrival rate of $(t)=5\mathrm{.}2-0\mathrm{.}01t[$with

$t$ in minutes after $7$:$50$ A$.$ M$.$ and $$

in vehicles per minute$].$ The toll

booth opens at $8$:$00$ A$.$ M $.$ and

serves vehicles at a rate of

$(t)=3\mathrm{.}3+2\mathrm{.}4t($with $t$ in minutes

after $8$:$00$ A$.$M$.$ and $$ in vehicles

per minute$).$ Once the service rate

reaches $10ve\frac{h}{m}$ in$,$ it stays at that

level for the rest of the day. If

queuing is $\frac{D}{D}\frac{?}{1},$ when will the queue

that formed at $7$:$50$ A$.$ M$.$ be

cleared?