We had at home when I was a kid an M&S book about cycling - it's about the only book I can't now find in my parents house, but as I recall it was softback and had a sort of graph paper design to the cover, with lots of people on bikes. Anyway, that said - as accurately as I can remember from 30 years ago "from the age of 12 upwards, any child should find 50 miles in a day to be not too much of an effort"
The kid (8) is generally fine when it's just us two and it's flat. Add other people and/or more than the most imperceptible of inclines into the mix and she is not happy. She did 6 miles in the summer to Boat of Garten, and she seemed ok, but we were with a group and being the slowest (and youngest) was a bother to her so when the opportunity to get the train back arose she was all over it. When it gets a bit warmer she wants to go out more - I've got her a new-to-her bike that that I've geared lower than her last bike as she never used 5th, and very rarely used 4th, but often wanted a 0 and a -1 so we'll see how that goes.
It's not a competition though - they do what they are comfortable with, and I guess it's our job to guide them re: do they want to do more but need encouragement, are they happy with what they can do and have no interest in doing more so it's counter-productive to try and make them, or are they really not that bothered about cycling and just doing it to be sociable with us? Or a bit of some or all of the above? I've suggested to the kid that when she's older we could cycle to my parents (TPT Sheffield to Manchester) and she has absolutely no interest whatsoever - just flat our refuses to countenance the idea that anyone would want to to do that when you could drive or go by train - but when I was talking to OH about maybe cycling the Great Glen Way at some point she was really keen. What's that all about?