http://www.reddit.com/r/explainlikeimfive/comments/1qb8gp/why_is_africa_so_far_behind/
And it's exactly how you thought a bunch of kids with a modern education would explain it.
Here's one explanation.
"[–]GoGoZombieLenin 19 points 35 minutes ago
Race is a social construct. All human life (as well as all other life on the planet) is one family. 200,000 years ago your ancestors and mine lived in Africa. Because of this Africa has the most genetic diversity. People from different regions of Africa can be more genetically distant from each other than from Europeans.
Racist ideology posits that different races are actually different species. They would consider interracial marriage the same as beastiality. This has nothing to do with reality. Speciation happens when populations that are geographically separated become so genetically different they can no longer produce viable offspring. Clearly this is not the case with humans."
Not everyone is buying it but they seem to be deleting a lot of answers. Everyone seems to be in agreement that Jared Diamonds Guns, Germs and Steel is excellent.