How long does it take the average person to achieve chess greatness?  If one where to study as if he/she was going to school or a university to learn; what would be the average time it would take someone to become a GM?

i would say 5 years +,

5 years would be normal if you study hard, alot and commited, and also you practice alot of tactics and positions etc..

Other then that i think it would take 5 years + just to achieve master strength, if you do not study hard but study enough.