Separate, but Equal: The School Cafeteria?

We did not have the chance to truly discuss Tatum's chapter on Black kids sitting in the cafeteria, but I would like to expound on it here. Interestingly, a teacher who I interviewed for my senior thesis commented on Central Catholic race relations by stating, "Among some of our students they can be -- there can be negative attitudes towards our Black students. I'll give you an example, you probably heard this many times. If a group of Black students are sitting together in the cafeteria that bothers White students . . . White students will say something like 'why are they doing that?'" Similarly, I have interpreted Tatum's analysis of Black students sitting together in the cafeteria as more of a White issue; meaning White students/administrators find it more problematic than Black students/administrators.

With the use of the school cafeteria and the condition of Black schools prior to Brown v. Board (pg 65 in Tatum's chapter on Black kids sitting together) How do you think Black America would have progressed if separate but equal was actual given a true chance? Is "separate, but equal" inherently unequal as the Supreme Court suggests or is it possible to truly have a separate, but equal environment? Is the cafeteria separate, but equal?