For a modern nuke boat (the only ones left) think highway speeds. There's nothing on the ocean that can keep up including all the escort cruiser/destroyers.
While in Ike (CVN 69), cruising the Med in 1988, we answered bells and hauled bootie from near France to off the coast of Lybia. We left the rest of the battle group behind. A nuke boat can move!
Cruised in JFK (CV 67) in 1990/1991, and while not as fast, she was fast enough. JFK's keel was laid as a nuke, but outfitted conventional because the family didn't want the name associated with nuclear anything.
A carrier typically only needs to be able to get 15 to 20 knots of wind over the deck to launch because the catapults are strong enough to fling an aircraft with enough airspeed to fly. Usually 5 kts or so above stall.
