Search Tranter's Corrections to Naismiths's Rule.
I'm sure you're already aware of this but the map shows horizontal distance. As soon as you get onto a decent gradient the distance you hike is greater than the horiz. distance shown on the map, so as well as likely going slower on the grade you're hiking further too. For example a 30 degree slope increase your distance travelled by 15%. (Naismith's, of course, takes this generally into account already.)
Hiking with one or more buddies can slow you down/speed you up according to their fitness, stops for photos/scenery/etc.
See if you can get/borrow a copy of the Mountaincraft & Leadership book. Has loads (or had: mine's 1984 vintage!) of good stuff on this topic., e.g. "A heavy pack can reduce progress by 50% of unladen speed, taking into account additional rest periods as well as speed over the ground. It is best to allow for this by simply estimating a slower speed, say 3 kph or even 2 kph in some circumstances."
Another consideration is how high you're hiking. For example, in North America you may be starting your hike at 8,000 feet or more and so altitude and its effects will impact your speed until you become more acclimatised. Temperature is another factor.
If you are in to tech. do a few sample and representative hikes, appropriately laden, with a hiker's GPS and note what it tells you for subsequent planning. Or even a wrist watch!
Or just do it...and enjoy the time spent on the trail!