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Lifetime high-points of my cycling include: 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.