Both sentence are correct but (technically) they have different meanings.
"Three times faster" means 3 times the base speed plus the base speed. If the base speed is 2 miles per hour, then three times faster is 8 miles per hour. [3 X 2] + 2
"Three times as fast" means 3 times the base speed. If the base speed is 2 miles per hour, then three times as fast is 6 miles per hour. [3 X 2]
In reality, the first one is used incorrectly probably more often than it is used correctly. Many people use the expressions to mean the same thing. Using "three times as fast" is the safer choice, because just about everybody understands that phrase.