It's actually very feasible; I once spent a summer riding close to 100 miles every day (and often more) and I don't consider myself extremely athletic (although I obviously got into pretty good shape that year): http://bybike.ca
The bicycle is the most efficient means of human transportation there is, in terms of distance/energy, as long as you have reasonably surfaced roads or trails.
I went and chose an office location that allows a 25 minute train ride, but the cycle ride following the river is far nicer and only takes an hour... so I do that instead (with the train as fallback if I'm having to make an exception once in a blue moon).
Riding != commuting, for me. I mean, being on a bike is nice, but going for a ride implies a more care-free attitude, and the complete liberty to go fast and sweat (there are no showers in the office). My favorite thing, once upon a time, was to just grab the bike in the morning and go.
I do 2h training rides (in full lycra, of course) before work, and we don't have a shower. Come to work, change all my clothes, put some water in the face, apply deodorant and I'm set.
I also cycle to work and do the same thing (change clothes, apply deo). Only a 25min or so ride though. I cycle differently to work than going back, makes it more interesting.
A century ride is actually pretty doable. It's somewhere between 5-10 hours for most individual, possibly a tad less if you're good and are riding with a group. You mostly just have to keep moving.
A double-century is a bit more challenging, but this is also a commonly encountered distance for recreational riders. Times tend more to 9-14 hours. At this distance, chafing and other discomfort can be an issue.
Elite cyclists may attempt 300 or more miles in a day, which does start to get a bit stiff.
I feel like such a lazy bum!!