I would think tracked PRTs would need less road space than driven cars. In medium density cities roads are a quarter of square footage. You could probably take out 1/2 or 2/3rds existing roads then and convert them to yards or parks.
Wikipedia says [1] high capacity road can carry 2,400 passengers per hour; light rail 20,000 - 25,000 passengers per hour per lane in each direction.
[1] https://en.wikipedia.org/wiki/Light_rail#Comparison_with_hig...