A rocket ship, on its way to the moon, can get up to almost 25,000 miles per hour in order to escape the Earth's atmosphere. However, it does not go that fast the whole way. Also, the ship cannot fly directly from the Earth straight to the moon surface. When it gets to the moon, the rocket needs to fly around and figure out a good spot to land. The first mission to stop on the moon with astronauts on it, Apollo 11, landed about four days after leaving the Earth surface.

Note: According to Wikipedia, Apollo 11 launched on 16 July 1969, landed on the moon 20 July, and returned to Earth on 24 July. The crew spent approximately two hours on the Lunar surface.

I believe I remember reading that the Saturn V rocket took around four days to make the trip to the moon. The moon is about 384,000 km from Earth. You do the math.

(The number I am getting in my head is a little less than one kilometer per second, or about 3,000 km/h, or about 2,000 mi/h)

I think that the Chinese are planning on repeating this particular experiment. We will see what they come up with. The Soviets tried it, but never made it.

The whole area of space travel, and all the research and missions carried out by NASA are really interesting. There is a lot of material you can read on these topics, I am sure your local library has more than just a few books. You might want to ask them.

I'll use the first successful mission to take men to the moon to answer your question. It took Apollo 11, that's the spaceship that carried Neil Armstrong, Michael Collins and Buzz Aldrin to the moon in 1969, 4 days 6 hours and 45 minutes to get to the moon. They took off from the Kennedy Space Center in Florida at 1:32 pm on 7/16/1969, and the lunar module landed on the moon at 8:17 pm on 7/20/1969. The speed needed for Apollo 11 to break free of the Earth's gravitational field was about 7 miles per second.

Apollo 10, a spaceship that only orbited the moon in 1969 holds the record for the highest speed attained by a manned vehicle with 11.08 km/s (24,791mph).

Thanks for this really interesting question.

The rockets that took the Apollo astronauts to the moon in 1969 took a whole day to get to the moon, and another day to get back.