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[LotR] Exactly how fast is Shadowfax?

This old bloke with a pointy hat just stopped by my village for water riding what he called "the Lord of all Horses", then zipped off towards halfling country.   
My donkey Bessie can manage quite the trot, but this Stallion was something incredible! 
For storytelling posterity, how speedy is that horse?
gpt
He managed to make the approximately 500 miles between Dol Baran (south of Isengard where the camp was made after the confrontation with Saruman) to Minas Tirith between the night of March 5/6 and dawn of March 9 while only traveling at night. This averages at around 10 or 11 miles per hour, but that's still an amazing endurance race over that time period.

It's also around 130 miles from Dol Baran to Edoras and that distance is covered in that first night of riding. Camp was made about 10 PM and if we assume that Pippin and Gandalf leave at around midnight, that leaves around 6 or 7 hours until dawn when they reach Edoras. That's an average speed of ~20 MPH, but again that's an endurance race, not a sprint.

There are endurance races for horse riding and an exceptionally good time for a 100 mile race is 10 hours. So, over a shorter distance than that first stage of Gandalf and Pippin's ride, the best "normal" horses average half their speed with the averages getting closer as we get to around 5 times the distance over many consecutive days, which normal horses would not be able to maintain.