Since warp speed is completely hypothetical, who knows what it really means to be "3 times as fast". The options are: it can reach warp factors 3 times higher, or it can reach speeds 3 times higher. Let's assume the latter. I remember reading somewhere that the speed scales as the cube of the warp factor: warp 1 is the speed of light, warp 2 is 8 times the speed of light, 3 is 27 times, etc...

So using this scale, "three times faster" could mean if the Enterprise top speed is warp 5, say (125 times the speed of light), the Dreadnought can travel 375 times the speed of light, or warp 7.2.