What time did the meeting begin and end?

Here is a problem that seemed pretty curious to me. I sat over her decision for more than one hour, until I gave up and looked at the answer. And here is the task itself: The

meeting began between 6 and 7 pm, and ended between 9 and 10 pm.
Determine exactly at what time the meeting began and ended if the minute and hour hands changed places during the meeting.