Well, that article needs some fact-checking, Stephen. According to what I found, in 1830 there was only 75.4 miles of railroad in the entire country, and the longest line, the Delaware & Hudson, extended only 16.5 miles. There was no such thing as interconnecting lines at that time. In 1857, while there was nearly 3,700 miles of railroad, the longest line was only 241 miles, from New York to Buffalo, but there was some opportunity to take connecting trains or travel by other means between railroad routes.
The reason for the increase in travel speed between 1800 and 1830 was improvements in roads, canals and the invention of the steamboat. The McAdam (macadam) paving process was developed during this time, which mean that roads didn't turn into mudholes whenever it rained and dustbowls when it was dry. Stagecoach companies came into being, and scheduled stages ran between cities and towns. Packet boats pulled by teams of horses on the canal system operated overnight between cities, which was gave an advantage over stages, which usually stopped overnight somewhere. And steamboats on navigable rivers also operated overnight.
Until the 1870's, trains didn't operate much faster than 25 or 30 mph due to track conditions, and as vast as this country is, at that speed, it took along time to get anywhere. In addition, until there was an economic need for a railway, it didn't get built. People were still reduced to travel by horse or stage to reach the vast majority of this country, and even at best, 15 mph was top speed for such conveyances. (In Pennsylvania's Cumberland Valley, the towns are spaced almost exactly 11 miles apart, the distance early settlers could easily travel in one day on horseback or by wagon.)