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On my reasonably flat commute I average around 16 mph on my road bike, but your average speed is dependent on many different factors. A general rule of thumb is that if you are switching from a mountain bike with knobbies to a road bike you will be between 15-20% faster at the same watts/effort.
If you look at the link, you will find that a very fit horse can go at a speed of 25 - 44 km/hr or 11 - 19 miles/hr. The horse page also notes that a fit horse is good for about an hour at that speed, which would cover the 10 miles that Rienzi galloped.