$5\mathrm{.}22$ 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?