Vehicles arrive at a toll booth according to the function $(t)=5\mathrm{.}2-0\mathrm{.}20t,$ where $(t)$ is

in vehicles per minute and $t$ is in minutes. The toll booth operator processes one vehicle every $20$

seconds. Determine total delay, maximum queue length, and the time that the $20$th vehicle to

arrive waits from its arrival to its departure.