>>93199Depends a lot on terrain, elevation, how many in your party, and your fitness level.
I usually do 15 to 20 miles a day when I'm out hiking, carrying about 30-35lbs of gear, but I limit my breaks, and that's when I'm traveling alone. Still, I can sleep in/be slow leaving camp in the mornings, and I usually have a couple of hours of daylight to set up camp/lounge/cook/nap before bed. I did about 15 the other day and spent about 1 1/2 hours eating lunch and drinking coffee by a creek, plus a few other brief exploratory stops.
I currently hike a lot, though, so that's probably close to the max I'll ever be able to do (or want to do).
I'd say at a reasonable pace, assuming an average level of fitness, some but not a lot of gear, and you're by yourself, 8-15 miles and you'd have plenty of time for breaks and sightseeing.
>>93615 is right about with girlfriend (or generally with any group, unless everyone is about the same level of fitness, experience, and mindset). Except I don't know what a km is. Killed miles? 
