Bailey: 22.74 mi/h
Johnson: 23.16 mi/h
This is a tough question. For those of you who watched the Olympic coverage on TV, you might have heard Bob Costas saying that Johnson ran the two parts of the 200m faster than Bailey did the one 100m in his race. This is the idea that the problem wanted to show. The velocities that we found are the average velocities and not instantaneous ones. Nobody had a radar gun pointed at these two men to see what their instantaneous speeds were, all we have are their dintances and times. While it is true that Johnson ran his 200m in less than double the time that it took Bailey for his 100m, the start throws things off. In both races, it takes time for the athletes to get to full speed. During this time when they are accelerating to their top speed, they are well below their average speed. Similarly when they are at their top speeds, they are faster than their average velocities. In the 100m, a larger percentage of the race is spent accelerating up to top speed, and the 200m has more time at the top speed, so their average velocities are not directly comparable. We have no way of knowing which runner is faster. My personal thought is that Bailey is the fastest as he won the shortest distance race. If Johnson wanted to be the fastest man in the world, then he should go for the triple, winning the 100m as well, then he would definitely be the world's fastest man.
The 100m race is a very interesting way of gauging speed. Carl Lewis is his heydey of winning the 100m always had bad starts and would be behind at the halfway point only to pass everyone with his superior top speed in the end. The start is so important in the 100m that it measures the body's reaction time as well as its flat out speed. Pitting Johnson and Bailey against a radar gun would sure be interesting. Then it would be all about flat out speed and not reaction times or the rate of acceleration.