Question $12$

Problem $4$: Determine the queue and delay information

USE THE PROBLEM STATEMENT BELOW TO ANSWER THE FOLLOWING QUESTIONS

A toll booth on a turnpike is open from $8$:$00$ A$.$M$.$ to $12$ midnight. Vehicles start arriving at $7$:$45$ A$.$M$.$ at a uniform deterministic rate of six per minute until $8$:$15$ A$.$M$.$ and from then on at two per minute. If vehicles are processed at a uniform deterministic rate of six per minute, determine the following:

Time when the queue will dissipate. Answer in minutes, round to nearest TWO decimals.