Unreal and incomprehensible. I take it those speeds are achieved while submerged?
Nuclear attack subs often times are assigned to a nuclear carrier task force as part of the perimeter defense. Nuclear carriers, when not conducting air ops, and in a hurry to get somewhere can crank it up to 35 knots plus. The only naval vessels capable of staying up with a nuclear carrier in a hurry is a nuclear attack sub running submerged.
Depending on design and a few other factors, most modern submarines can travel faster submerged than on the surface. In fact... you'll have a tough time finding a "bubblehead" who likes to spend any more time on the surface than necessary (not a lot of "lateral stability" in the hull design if you know what I mean)
The smilie face you saw on a couple answers re: speed and depth are because the information is classified. Those who really know aren't going to tell you... and those who tell you likely don't know. :)
So you get canned answers like "deeper than 800 feet" or "faster than 20 knots".
Suffice to say that the performance of modern submarine designs is phenomenal.