It's an old enough tradition that there are jokes that rely on you knowing the tradition.
My favorite: professor known for being VERY strict tells class repeatedly in weeks leading up to exam, "You will have exactly two hours to finish your exam, and no more. I will not accept exam booklets turned in even one minute past the two hour mark: they will score a zero. Be warned."
Exam day comes, and all but one student are in their seats with the blue exam booklet in front of them when the professor says "Begin." He arches an eyebrow at the empty desk, but says nothing.
Fifteen minutes later, the tardy student rushes in. "Family emergency," he says, "sorry." The professor tells him "You have one hour forty-five minutes." Student says nothing, but opens his book and starts writing furiously.
The two hour mark comes up, and everyone except the tardy student turns in their booklets and leaves the room. The professor reminds him "Time's up," but he just keeps writing in the booklet.
At the 2:12 mark, one hour fifty-seven minutes after he ran into the exam room, the student closes his blue book and walks up to the desk where the other books are stacked up in a messy pile. The professor is reclining in his chair with his feet up on the desk. "Nope," he says, "you're late. I won't accept your exam booklet, and you're going to get a zero on the final exam."
"That's not fair," said the student, "I had to drive my mother to the hospital. I shouldn't be punished for that. I took no more time than anyone else."
"Nope, you knew the rules," says the professor.
"Don't you know who I am?" says the student, raising his voice.
"Nope, don't know, don't care," says the professor.
"Good!" says the student. He slides his exam book into the middle of the messy stack, straightens it up neatly, and before the professor has gotten his feet off the desk, walks briskly out into the hallway.