No, the point is that if you hit 25,000mph in low Earth orbit you are then going fast enough to reach an indefinite distance away from the planet without further need for acceleration - not that you will continue moving at 25,000mph because you have magically escaped all influence from Earth’s gravity.

When you fling an object upwards it immediately starts accelerating downwards under gravity. The higher its initial upward velocity, the higher it will reach before this acceleration brings it down. For slow moving objects close to Earth acceleration due to gravity can be considered a constant 32ft/sec/sec; for fast moving objects you have to factor in the lesser effects of gravity as altitude increases. But there’s still plenty of Earth gravity about the place by the time you get as far out as the Moon; enough to constrain the Moon to a 29-day orbit about the planet.

Bottom line: Crank your rocket up to 25,000mph and you’ve enough velocity to slip the surly bonds of Earth all right, but you’re slowing down steadily as you move away - you decelerate quickly at first, more slowly the further away you get, and at this particular speed it will take until you reach an “infinite” distance from Earth before you slow all the way down to zero. So most of the trip to the Moon was made at a speed a good deal less than 25,000mph.

It didn’t take that long to reach this speed. They got up to Earth orbital speed - 17,000mph - in just a few minutes starting with a brutal 4g acceleration from the first stage that gave them over 5000mph in a couple of minutes IIRC. (Accelerating at that speed you’re adding 80mph to your speed every second.) So they had only to add the remaining 8000mph, and at a modest 1g acceleration that would take only *does the sums* six to seven minutes or so. I’m not sure what the actual figures were, but there is info about all this somewhere on the Web.