How much time do you have to swing at a 100 mph fastball?

about 0.4 seconds

90 feet from pitcher to batter --> no, it is 90 feet along the base paths, but it is 63.6396 feet from the pitcher's mound to home plate

100 MPH = 146.666667 Feet Per Second

63.6396 ft / 146.6667 ft/s = 0.4339 seconds = time pitched ball to reach batter

so if you factor in that the batter has to first see the ball, detect its a fastball, recognize its location, and if in the strike zone, attempt to hit it (all in less than a second), you can probably agree: "man, these guys are good"