Zach and the others pulled an all-nighter, searching through the sewers for any signs of the Underworld before calling it for the day. It was disappointing that they hadn't found anything, but they had only covered a fraction of the sewers. It was a sizeable fraction, but a fraction nonetheless.
So, they returned to the Academy in time to clean up and sanitize themselves before they had classes. Even as a fourth year, Rabst still had proper lessons about things that were important to learn, like etiquette, language, and math.
Zach didn't care much for the lessons that weren't related to the Underworld or monster studies. He had his background as a noble and, thanks to his upbringing, he had no trouble staying at the top of class, even if he didn't study.