Explain how the supreme court justified the practice of segregating railroad passengers in louisiana

The practice of segregating railroad cars was decided in the Supreme Court case Plessy vs Ferguson. In this case, Homer Plessy argues that even though he is 1/8th African-American, he should still be able to sit in the 1st class white section since he paid for a ticket there. The Supeme Court ruled against him stating that cars can be separated by race as long as they are equal. This concept of separate but equal became wildly popular in the US and was used in schools, restaurants, etc.