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Don't mind the people
But public transit averages about 12 mph because it stops all the time, and switching lines on a PT system can often take a lot of time, worse if the schedules are unreliable. Surface transit of course also hits traffic like cars.
The PRT idea was conceived long ago. Today there is some argument that self-driving, crash-avoiding cars may realize this vision on ordinary roads.
But the big plusses over both transit and taxis are the fact it doesn't stop, you rarely wait for it to arrive, changing lines is like changing highways, and it has private right-of-way to avoid traffic. Compared to the car it also does not have to be driven, so you can work.
The proponents also say it's considerably more energy efficient than transit, primarily because it doesn't have to start and stop all the time, and while there is waste sending empty cars around to new stations, you don't spend most of the day with large underutilized train cars and busses like transit does.
That's the theory, anyway.
But because transit gets such a low net speed (measured in average trip time, including waiting and stops) for short-haul in particular, the PRT doesn't have to be very fast to beat it handily. A 20 mph PRT would typically beat street cars and busses as well as ordinary cars in anything but light traffic, and even private right of way trains if there's wait times or line changes.