If i say I’m going to do something at noon, how long do I have available to do it?

If I say I am doing 2 different things at noon, am I wrong?

Noon is an exception, to me, noon lasts an hour. Most top(and bottom)-of-the-hours last 20 minutes – from 10 to until 10 after (quarter to or after then, lasts 10 minutes).

I don’t think I’m wrong to say I will leave the house, stop at my office (3 minute drive away) and then go pick up the mail (a 5 minute walk) at 1.

Problems arise when two people have different ideas about how long time lasts. As in:

“What time are you leaving?”
“9”
“Are you leaving at 9:00 or getting to your office at 9:00?” (remember it’s a 3 min drive).
“Same thing”
“No it’s not. In one case you leave at 8:55 (in case of contingencies) and in the other you leave at 9.”
“I’m leaving when I’m ready”
“When will that be?”
“9”
Frustration on both sides.

How long does a time last?