When you want to travel to the third world countries that connect the cities of the US you could rent a car, which is necessary because rural areas have apparently forgotten about public transit of any kind. In civilized countries, there's a solid network of mass transit basically everywhere. It doesn't matter that you're in a podunk town, a bus comes by every half hour because it's a necessity to have a regular bus more than a full one.

Then you take the train. If this is not an available option, you take the car, one of which you either own but barely use when staying within the city, or that you buy (which is the option I chose, it's a lot cheaper than to own one).

There also should absolutely be trains that connect cities together too, it's already mostly the case in Europe which is around as big as the US, including high speed trains between major cities, but there is also a lot of regular trains that connect moderately sized towns with their nearby city. This can be both a cheaper and faster alternative to driving a car if you go somewhere you won't need a car (say, a city with very good public transit). China may be more comparable to the US as it is a single country with a similar size, but the size of their train network grew tremendously over the last twenty years, especially their high speed network. I guess a good start for the US would be to connect the major cities on the East Coast with high speed trains, such as DC, New York, Chicago, and other cities nearby, I can guarantee you there will be demand for that.

In fact, I'm about to take a high speed train from Paris to Lyon. Including the time I'll have spent in public transit to go to and come back from the train station, it'll take me three hours total vs four and a half hours by car without stops on traffic jams to travel some 400km (around 250 miles). The tickets cost me 90€ both ways, including the subway and tramway, while the same travel by car would cost me at least that much in not double.

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