The LT guide lists estimated hiking times between shelters. Just for fun I added up all the times to see how long you'd have to hike to do the whole LT which turn out to be 179.75 hours.
Now if you hike for 8 hours a day, it will take 22.46 days to do the trail. Since the trail is 268.3 miles long, that works out to be 11.94 mpd.
The estimated hiking times are fairly conserative, so most people can beat those times and due to shelter spacing it's not going to possable to hike exactly 8 hours a day. But in the end, I think the 22 days to do the LT is pretty close to an average time.