Track how far a horse can travel in a day.
So, a "day" is 24 hours and a long rest of 8 hours. According to my calculations, that's 2 travel periods:
How to travel 8 hours (12-8), then rest 8 hours (sleep? 8-4), then a second 8 hours (4-12) of travel
Since RAW a horse can travel 34 miles in 8 hours: 7 hours at a fast pace for 28 miles, then 1 hour gallop for 6 miles, a total of 34 before you need to rest.
Would this allow the total travel distance to DOUBLE (at 60 or 68 respectfully), if the party focused 100% on traveling for 24 hours in a row, assuming they used my previous example method?