Well, Batman had no problem gunning down a criminal with a machine gun in the dark knight.
I dont know how fast the cars are in speed racer, but i always imagined they topped out at jet speeds, but i guess if it's a death battle with cars, batman always wins. If it's a race, i dont think batman has the slightest chance.
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He's a professional driver, and his car is modded for all kinds of terrain. In the Speed Racer movie, they were driving on walls, up mountains, and jumping all around the tracks. Racer X himself was able to outdrive a team of drivers attempting to take him down with giant maces, guns, and even attempting to crush him with the cars themselves. The Batmobile isn't made to race I believe.