Visualize a lively shopping centre with an automatic photo booth as its focal point. The booth has a bright green light that signals if it's ready for customers. People are forming a queue in front of the booth, all eager to get their photo clicked. Imagine the first person in the queue inserting their money into the booth, causing the green light to turn off. Illustrate the concept of time passage in the scene by using subtle cues - maybe the positions of the sun, changing expressions of waiting people, etc., to indicate 15 minute intervals.

There is an automatic photograph booth in my local shopping centre. It takes exactly 2 minutes

from the time that the money is inserted for the photographs to be taken, then the developed
photographs appear 4 minutes later.
Money may only be inserted when the green light is on. This light goes out immediately after
money is inserted, and comes back on again exactly 3 minutes later.
This morning, I arrived at the booth just as it was being switched on, and I was sixth in the
queue. The first person inserted their money immediately, and the rest of us all inserted our
money as soon as we were allowed to.
How long after I arrived at the booth did I insert my money?

so, at 3 minutes per person ahead of you, you waited 5*3 = 15 minutes

Extra credit: How long did you have to wait for your photos?

Well, let's break it down, my friend. The first person in the queue inserted their money right away, so they had to wait for 2 minutes for the photographs to be taken. Then, they had to wait an additional 4 minutes for the photographs to be developed. That's a total of 6 minutes.

Now, here's where it gets interesting. The green light comes back on exactly 3 minutes after the money is inserted. So, let's do some clown math here. If the first person inserted their money and had to wait 6 minutes in total, that means the green light came back on 3 minutes after they inserted their money.

Since you were sixth in the queue, my friend, that means you had to wait for the five people ahead of you to insert their money and wait for the green light to come back on. So, if we add up their waiting time, which is 5 × 3 minutes, we get 15 minutes.

Now, you need to account for the time it took for the previous people to have their photographs taken and developed. That's a total of 6 minutes each, which gives us 5 × 6 minutes, which is 30 minutes.

So, if we add up the waiting time for the green light to come back on (15 minutes) and the time it took for the previous people to have their photographs taken and developed (30 minutes), we get a grand total of 45 minutes.

Therefore, my friend, you inserted your money 45 minutes after you arrived at the booth. I hope you managed to find some comic relief during that time!

To determine how long after you arrived at the booth you inserted your money, we need to calculate the time it took for the first five people to insert their money.

Given:
- It takes exactly 2 minutes from the time the money is inserted for the photographs to be taken.
- The developed photographs appear 4 minutes later.
- The green light comes back on exactly 3 minutes after money is inserted.

Let's break down the time for each person:

1st person:
- Inserted money when the green light was on.
- Waiting time for the green light to come back on: 0 minutes.
- Time for photographs to be taken: 2 minutes.
- Time for developed photographs to appear: 4 minutes.
Total time for the 1st person: 0 minutes (waiting) + 2 minutes + 4 minutes = 6 minutes.

2nd person:
- Inserted money when the green light came on after 3 minutes.
- Waiting time for the green light to come back on: 3 minutes.
- Time for photographs to be taken: 2 minutes.
- Time for developed photographs to appear: 4 minutes.
Total time for the 2nd person: 3 minutes (waiting) + 2 minutes + 4 minutes = 9 minutes.

3rd person:
- Inserted money when the green light came on after 3 minutes.
- Waiting time for the green light to come back on: 3 minutes.
- Time for photographs to be taken: 2 minutes.
- Time for developed photographs to appear: 4 minutes.
Total time for the 3rd person: 3 minutes (waiting) + 2 minutes + 4 minutes = 9 minutes.

4th person:
- Inserted money when the green light came on after 3 minutes.
- Waiting time for the green light to come back on: 3 minutes.
- Time for photographs to be taken: 2 minutes.
- Time for developed photographs to appear: 4 minutes.
Total time for the 4th person: 3 minutes (waiting) + 2 minutes + 4 minutes = 9 minutes.

5th person:
- Inserted money when the green light came on after 3 minutes.
- Waiting time for the green light to come back on: 3 minutes.
- Time for photographs to be taken: 2 minutes.
- Time for developed photographs to appear: 4 minutes.
Total time for the 5th person: 3 minutes (waiting) + 2 minutes + 4 minutes = 9 minutes.

Now let's calculate your time:

Total waiting time for the first 5 people: 6 minutes + 9 minutes + 9 minutes + 9 minutes + 9 minutes = 42 minutes.

Since you were the 6th person in the queue, it means that you had to wait for all the previous 5 people to finish. Therefore, the time it took for you to insert your money is equal to the total waiting time for the first 5 people.

Therefore, you inserted your money 42 minutes after you arrived at the booth.

To determine how long after you arrived at the booth you inserted your money, we can analyze the sequence of events and calculate the time intervals.

1. The first person in the queue inserted their money immediately.
2. The green light goes out immediately after money is inserted.
3. The green light comes back on exactly 3 minutes later.
4. The developed photographs appear 4 minutes after the photographs are taken.

Let's break down the time intervals:

- From the time the first person inserted their money until the green light comes back on: 3 minutes
- From the green light coming back on until the developed photographs appear: 4 minutes

Since the first person inserted their money immediately, we know that when the green light comes back on, it has been a total of 3 minutes since the booth was switched on.

In the given scenario, you were the sixth person in the queue. Therefore, you would have inserted your money after all the people in front of you have completed their transactions.

Number of people in front of you: 6 - 1 (the first person) = 5

To calculate the time it took for the first five people to complete their transactions, we can sum the time intervals:
5 people * 2 minutes per transaction = 10 minutes

Since you arrived just as the booth was being switched on, you need to add the time it took for the green light to come back on:
10 minutes (time for the first five people) + 3 minutes (green light coming back on) = 13 minutes

Therefore, you would have inserted your money 13 minutes after you arrived at the booth.