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I bike to work. Well not directly to work, to the subway station where I take the train to work. I park my bike in a locking cage with a key card that costs 5 cents an hour to park (parking in the lot costs $3/day)
I ride in the same basketball shorts and an athletic "breathable" t shirt even though it's winter where it's high 30s-low 40s in the morning. Put my work clothes (just a pair of jeans and polo/collared shirt) in my backpack with my lunch. I wear sneakers when i ride and I wear these autistic rain covers to avoid touching the chain and ruining my shoes with grease.
My commute isn't very long, it's only about 4.5 miles. But it is a 700 foot change in elevation (pic related, downhill to station in morning takes about 15 minutes, uphill back home takes about 25-30 minutes). Even after riding this route for over a year or year and a half, I still can't do the uphill home any faster and only average usually around 11.5 mph.
It's great when I ride the main boulevard back home and it's bumper to bumper traffic and I pass by people. I've had a few times where people stop me at the cage and say they do the same commute home and how quickly I get back (lol) and how great it is I do it for exercise.