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The average horse can run at about 30 miles per hour. Horses that are bred to run long distances have been recorded to run up to 40 miles per hour. Quarter horses bred for racing short distances have been reported to run as fast as 50 miles per hour. The highest race speed is recorded at 43.97 miles per hour by Winning Brew in Grantville, PA. on May 14, 2008.
Endurance horses can go 100 miles in 10-12 hours, so if your horse is super fit, he could go 100 miles a day (he would be too tired to go all 24 hours, so we'll say 100 miles a day) so 300 miles in 3 days.