The different races came through time by natural adaptation from the three sons of Noah who went in different directions. The Bible explicitly states that all humanity are the descendants of Noah through his three sons.

Gen 9:18-19 “Now the sons of Noah who went out of the ark were Shem, Ham, and Japheth. And Ham was the father of Canaan. These three were the sons of Noah, and from these the whole earth was populated.”

The account of Genesis 11 is found in Genesis 10. Gen 10:1 Now this is the genealogy of the sons of Noah: Shem, Ham, and Japheth. And sons were born to them after the flood.

Gen 10:5: “From these the coastland peoples of the Gentiles were separated into their lands, everyone according to his language, according to their families, into their nations.

Gen 10:20: “These were the sons of Ham, according to their families, according to their languages, in their lands and in their nations.

Gen 10:31-32: “These were the sons of Shem, according to their families, according to their languages, in their lands, according to their nations. These were the families of the sons of Noah, according to their generations, in their nations; and from these the nations were divided on the earth after the flood.”

We can trace the genealogies of  all the numerous races back in time-- This is the genealogy of Shem: Shem was one hundred years old, and begot Arphaxad two years after the flood. (Gen 11:10)

Different racial skin tones did not originate at the Tower of Babel,

There were two different exodus,' one from Noah's family and the other from those at the Tower of Babel. So the LORD scattered them abroad from there over the face of all the earth, and they ceased building the city. (Gen 11:8)

 The event at the Tower of Babel caused humanity to be scattered throughout the world; and as they went to different parts of the world different factors came into place. Environmental adaptation and the passing on of acquired genetic characteristics effected different racial skin tones.