You are WAYYY off base. Carriers are WAYYYY faster than most ships! An old sea story, from the 70s: A US Naval Destroyer, at dawn, noticed a Soviet gas-propelled hydrofoil off of the starboard(right) side of the Ship.
The Soviet used the Light System to send Morse Code: “Where is Kitty Hawk?”. Apparently, it had been assigned to shadow the Carrier. The Signalman turned to the OOD, and asked him how he wanted to reply.
The OOD said, “North Carolina, USA!”.
Overnight, US Carriers in full EMCON-no ligts, no radar, etc., can disappear and be hundreds of miles away.
Carriers are typically much faster than other ships. When I was in the Coast Guard I was stationed aboard a High Endurance Cutter – 378′ in length.

One of our missions was National Defense, specifically as an Anti Submarine Warfare platform. Because of that, we participated in war games with the Navy and were part of the carrier’s defensive screen. This was in the mid-70’s. Our ship was one of the first class of vessels to be outfitted with gas turbine engines to give us greater speed when we needed to get somewhere fast.
Normally we cruised on diesels, but we could spin up those turbines when we needed them. When we cruised with the carrier, we needed them, and even with the turbines (essentially jet engines) kicked on, with 12′ rooster tail behind us, we could barely keep up.
