I hope I am understanding what you mean, if not, I apoligize.
So, first off, Whites could attend any school they please, all of their schools would be closer to their home and they would not have to travel far. For the Black community, they might have to travel a few hours to get to school each day, as the closest black school might be far away.
Second, white-only schools had better buildings. They were cleaner, they got the better funding from the state, they got higher quality education and the list goes on. Since each district determines the funding of the school, it would make sense that the white section would have more funding. Black people back then could not get super high-paying jobs, and the houses they could choose from within the black section were not very nice and neat. Making it in more of a poverty section, this meant less funding for the school.
I'd reccomend looking into Brown v. Board of Education too, since these topics can be closely related to each other. Notice the pictures below and the differences within the schools, the white school has proper desks, whereas the black one has only seats.
