We have core hours here too. 9:30-3:30 are "core hours" and you must be in the office during those hours. However, lately I have an 8am meeting every day, so I need to be in by 8am at the latest.
I live a 10-12 minute ride, 35 minute walk, 10 minute bus, or 7 minute car ride from the office, so I don't have a LOT of problems getting in on time. Worst case scenario is I ask my husband to drive me because I'm really late (and/or it's really bad weather).