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.

This sounds like a queueing process.  You could model two separate processes $-$ the arrival time of the student and the departure time of the tram $-$ and use these to construct a model for wait times (the difference between departure and arrival times).  Alternatively, you could model the wait times directly.  Typically processes of this nature are modeled with skewed distributions like exponential or gamma.  If you had actual data it would advisable to view a histogram of your data to get a sense of what model would fit best.
