What time did the meeting start and end?

Here's a problem that seemed to me rather curious. I spent more than one hour on her decision until I gave up and looked at the answer. And here is the task itself:

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