3 times a week? Entirely possible. We don't own a car (if necessary, I can get a bus/train into town and grab one from a car sharing scheme), and usually do everything by bike (or with public transport).
I work 5 days a week and have to go over a distance of roughly 10 miles, with ~200 meters (600 feet) of height difference between my workplace and home (downhill going to work, uphill on the way home). An acquintance from the local bike club only has three days of commute per week, but commutes ~30 miles (one way) over flat terrain.
During winter (i.e. now) I'm using a modified unsuspended MTB (finally built one myself from a good steel frame and the parts that accumulated and survived over the last few years), during summer (i.e. without risk of ice or salt on the roads) I ride a touring recumbent.
Exhausting? Just take it slow. The difference between pushing it and going leisurely is maybe 5 minutes on my daily ride.
Monotonous? Much less than in a car (or the train). Ok, on the bike I (usually - unless it's covered in ice like today) take the scenic route for most of the trip.
Hate life? Definitely not.
Aching muscles? No. Ok, sometimes - two times per year, for about a week or so, after I've switched between the two bikes. Recumbent uses other muscles as the MTB (and vice versa), especially in the neck (on the 'bent, I have to look 'down', on the MTB, I need to look 'up' in order to see the road).
Athletic? You wish... I could afford to lose 20 kilos, and I'm 20 years older than you are.