Lifetime high-points of my cycling include:
- maximum distance in one day: 108 miles (ride across Florida)
- fastest averages: (average does NOT include breaks)
- 15.5mph over 50 miles (Skokie trail, 2008)
- fastest averages: (including breaks)
- 17.2mph over 5 miles (Skokie trail, 2008)
The 108-miles-in-one-day was done alongside multiple people who had previously gone a maximum distance of 10 miles in their life. So, while impressive, it was more a test of dedication than of endurance-through-training.
So, what's called for is either doing extremely long rides (150-200 miles) in one day, or doing longer and longer rides at ~15mph average (preferably INCLUDING breaks).
Trying to do 200 miles during daylight (even in summer, Chicago has ~15.5 hours of daylight) would mean that you'd have to average 14.5mph. Of course, many long rides go all-night, and 200 miles can be done within 24 hours at the sedate pace of 8.33mph, so one perhaps should focus on average speed rather than massive distances.