Longest run I've seen (posted in another comment above) starting in NW Montana: https://river-runner.samlearner.com/?lng=-113.26136901231438...
5570 km (3461 miles)
Rivers fluctuate between 3 to 15 mph on average (quick Googling).
At an average of 3mph: ~48 days
15mph: ~9.6 days
7mph: ~20.6 days
I'm sure the time of year you decide to run the experiment would change the results pretty drastically.
