show step by step how they came to the answer: and show the math behind the work

Inner City Adventure is one of the many projects of Social Enterprise Lab. Construction of the amusement park just east of downtown Los Angeles is complete except for the restaurant. You are hired by the project as a process consultant. (You work pro bono of course) According to the current business proposal, a typical park guests experience will be as follows:

A guest comes to the park gate to purchase a ticket. There are three ticket agents each of whom can sell a ticket to a guest in 30 seconds on average.2 It takes 2 minutes on average to get a ticket (wait time = 1 min 30 sec and process time = 30 sec). Because of the small size of the park, there are only two attractions in the park Its a Tiny World and Galactic Magnum Mountain.

Its a Tiny World takes exactly 4 minutes, and 40 guests can enjoy the ride at one time.3 Before a typical guest can enjoy Its a Tiny World, she has to wait 8 minutes on average in line.

The other attraction Galactic Magnum Mountain takes exactly 3 minutes, and 15 guests can enjoy the ride at one time. There are, on average, 15 guests here, including those guests waiting and those who are enjoying the ride.

Because of the awkward land, the park is designed such that each guest enjoys only one of the two attractions. After enjoying a ride, some guests go to the restaurant to try the famous European gourmet sausages while others who are not hungry leave the park without eating.

After market survey, the project team learns that 90 guests per hour will come to the theme park, a half of whom will enjoy Its a Tiny World and the other half Galactic Magnum Mountain. The survey also finds that only 5% of the guests who enjoy Its a Tiny World will dine at the restaurant while 15% of those who enjoy Galactic Magnum Mountain will. Those who eat will spend 30 minutes in the restaurant, that is, FT = 30 minutes including waiting time and eating time.

Now the project team has to decide how many seats they should have in the restaurant. The current construction plan indicates that they will have 20 seats.

How many guests are there on average at the ticket counter, including those who are waiting and those who are buying tickets?

Answer: 3 guests

How many guests are there at Its a Tiny World, including those who are waiting before the ride and those who are enjoying the ride? Answer: 9 guests

What is the flow time for Galactic Magnum Mountain, including the wait time and the 3-minute ride duration? Answer: 20 minutes

What is the flow rate at the restaurant? Answer: 9 guests/hour

How long do guests spend on average at the theme park (overall flow time)? Answer: 21 minutes