Its the poor class that uses public transit because it is substandard, and they dont have other choices.
Public transit is substandard because public transit has to fight on the regular roads, and not dedicated track/roads for transit. This means it is innately as slow or slower than driving. Because of this, it anyone who has a car WILL TAKE A CAR.
For example, it takes me 20 minutes to go from 1 side of the city to the other. Using the bus routes, its 2 hours. This is the predominant reason why people don't use public transit - 6 times longer.
Free is an essential start, though.