Why was Hagrid kept waiting for half an hour?

Question

The detention in The Philosopher's Stone was clearly set for eleven o'clock.

Your detention will take place at eleven o'clock tonight. Meet Mr Filch in the Entrance Hall.
Prof M. McGonagall
_{(Philosopher's Stone, Chapter 15, The Forbidden Forest).}

Filch accompanies the kids down to Hagrid's hut. Hagrid complains that they're late and says he's been waiting for them.

"Abou' time," he said. "I bin waitin' fer half an hour already. All right, Harry, Hermione?"
"I shouldn't be too friendly to them, Hagrid," said Filch coldly, "they're here to be punished, after all."
"That's why yer late, is it?" said Hagrid, frowning at Filch. "Bin lecturin' them, eh? 'Snot your place ter do that. Yeh've done yer bit, I'll take over from here."
_{(Philosopher's Stone, Chapter 15, The Forbidden Forest).}

Why did Hagrid think they were late? Had he been told the wrong time? Were they late? It seems odd that he should be hanging around for such a long time for them when the time was agreed in advance.

Answer 1

Two paragraphs after Professor McGonagall sends the notes:

At eleven o'clock that night they said goodbye to Ron in the common room... (Philosopher's Stone, Chapter 15)

This implies that they did not leave early to meet Filch or be at detention by 11 pm. I posit that this is how the characters interpreted the note two ways:

1. The detention was scheduled to start at 11 pm and the Gryffindors left late from misinterpretation. It seems odd that Filch or Malfoy did not complain about tardiness or that Hermione is not concerned about being late.
2. They were to meet at the Entrance Hall at 11 pm and Hagrid was misinformed about the location.

Either way, the Gryffindors left late. Taking into account distance from the dorm to the Hall to Hagrid's hut they would appear to be 30 mins late by Hagrid's count.