Famous historical example
... of one fleet leaving after another but arriving at the destination earlier, although both fleets had the same kind of ships.
The year is 1798. The French fleet rules unopposed on the Mediterranean Sea. The British send an expeditionary fleet in the Mediterranean with the goal of intercepting and engaging the French fleet.
On 19 June 1798 the French fleet commanded by Vice Admiral François-Paul Brueys d'Aigalliers left the freshly conquered Malta heading for Alexandria in Egypt, carrying an invasion force intending to conquer Egypt and the other Ottoman possessions in the Levant, with a view of opening a French-controlled route to India.
On 22 June, the British fleet, which was at that time was near the southernmost point of Sicily, got word (from a Genoese merchantman out of Ragusa) that the French had sailed for Alexandria. Rear Admiral Sir Horatio Nelson ordered the fleet to Alexandria at top speed, hoping to catch the French while they were still disembarking the troops.
The British fleet arrived at Alexandria on 28 June. The French were not there, and nobody had even heard of any invasion force.
Nelson spent the next month searching for the French fleet around the Anatolian coast, around the Greek coast, and around Sicily; finally, on 28 July the British fleet (which was then somewhere near the Peloponnese) received a notification (from the Ottoman governor of Crete) the the French fleet had been seen at the end of June sailing south of Crete towards Alexandria.
Nelson odered the British fleet to sail to Alexandria again, and again at top speed. On 1 August they sighted the French fleet at anchor in the Bay of Aboukir and the rest is history.
What had happened was that:
The British fleet was sailing much faster than the French fleet. They had the same kind of ships, but by and large British naval officers were much better at coordinating fleet movements, with the effect that British fleets could (and did) move faster than French fleets.
The British fleet had overtaken the French fleet on 22 June; at dusk, they had seen the sails of four unknown ships. During the night, the British fleet continued sailing at speed, while the French reduced sail because of course that's what one does when it's dark outside and one needs to be cautious against potential navigation hazards which may have been lurking in the eastern Mediterranean undiscovered for three thousand years despite of continuous and intense navigation. (OK, there was some fog too.)
In the morning, the British looked around for strange ships but saw nothing, because by that time the French were dozens of miles behind.
Upon arriving at Alexandria on 28 June, Nelson made his enquiries, got his answer that nobody knew anything about any French fleet, and left promptly on the next day. Unknown to him, the French, instead of sailing directly from Malta to Alexandria, had taken a sight-seeing tour around Crete (with the express intention of not sailing directly to Alexandria, to make any enemy scout doubtful about their true intentions) and arrived two days after the British fleet had left.
Key points to remember:
Fleets do not normally move at top speed. They generally move at the best economical speed, which provides a good compromise between speed and endurance.
Even when a fleet moves at top speed, its top speed is the top speed of the slowest ship in the fleet.
Fleets need to maintain cohesion and order. The top speed of a fleet is lower than the top speed of an individual ship, because the fleet needs to coordinate ship movements, take corrective actions when one or more ships get displaced, send scouts to look around and come back and so on.
Very often it happens that a fleet will avoid sailing on a direct course to the destination, with the intention of making it harder for the enemy to guess where the fleet is going.
(Read all the entracing details on Wikipedia.)