$1$

$.$

$$A TSA officer verifying ID and boarding pass

$2$

$.$

$$Searching the passenger for metal objects

$($

security scan

$)$

The passenger is going through a metal detector, which is staffed with another designated TSA officer who watches the screen and performs the pat

$-$

down search if needed

$3$

$.$

$$Running the carry

$-$

on luggage through X

$-$

ray machine

There is a long line of passengers before the first step, but sometimes lines also build up at steps

$2$

$$and

$3$

$.$

$$Step

$2$

$$and

$3$

$$are parallel; that is customers go through the metal detector while their luggage is in the X

$-$

ray machine. $($e$)$ As before, assume that there are many customers waiting in the process $($i$.$e$.,$ the demand exceeds the capacity$).$ What is the average cycle time? Express your answer in seconds, round to two decimals if nee