What distribution is the most appropriate? I am given the following problem:

A student S wants to take the tram to go home after his lectures are
over. The tram line he’s used to take leaves every 7.5 minutes on
average at the university. Unfortunately, student S cannot remember
the departure times. Thus, he always arrives randomly at the tram
station every single weekday.

I am then asked the question which distribution is the most appropriate one to model the daily waiting times of the student.
The random variable $X$ reflects the daily waiting time. I thought about an uniform distribution with $a=0$ and $b=7.5$ since the student arrives randomly at the tram station and thus has equal probability for every waiting time between $0$ and $7.5$.
So far so good. What is confusing me though is the fact that the arrival of the tram is again a random variable (the tram only arrives every 7.5 min on average). So I am not exactly sure how to model this as the upper bound $b$ of the uniform distribution would not always be exactly $7.5$  but rather a realisation of the underlying distribution.
I hope someone can explain how I can model this accurately.

Assuming that the trams are independent on each other and runs the same way 24/7, their arrivals can be modeled as Poisson process, whose inter-arrival time follows exponential distribution with mean = 7.5 minutes.
Student S entering the queue every day can be considered as a resampling of the process with a random shift t, which does not impact the underlying inter-arrival distribution.
