At ~90/95 mph, the ball travels from the pitchers mound to the plate (60ft. 6in) in 400 milliseconds. After calculating the time it takes to look and think, the batter only has a quarter of a second to decide what to do or not and start the swing. The swing itself takes 150 milliseconds, so the batter must start his swing approximately 25-30 ft in front of the plate. The ball will arrive at the plate about a quarter of a second later. Test you reaction skills and whether or not you could make the 90 mph hit here: http://www.exploratorium.edu/baseball/reactiontime.html
The margin of error is a whopping 7 milliseconds- too early or too late and you'll hit it foul. So next time you're watching baseball and a player hits a 90 mph fastball, appreciate how hard that is to do.
The link to the diagram explaining all of this is: http://ncaabbs.com/showthread.php?tid=289453