Moon+Trips

How long did it take to get to the moon and how fast did they go? If escape velocity from Earth is 25,000 mph and the moon is 250,000 miles away, shouldn't it only take 10 hours to get there? Why did it take the Apollos 70 hours?

The spacecraft did not travel at 25,000mph all the way there. Escape velocity is defined as the speed you need to reach to escape with no further active propulsion from the engine. If you have a continually firing engine you can escape at any speed you like. However, fuel economy requires a big boost followed by coasting for the rest of the trip.

The launch used the first two stages and some of the third stage of the saturn V to get up to 17,500mph, orbital speed. After a couple of orbits to check the systems the third stage reignited and accelerated the spacecraft to 25,000mph. It took about ten minutes of firing to do that. After that point the spacecraft was unpowered, and subject to Earth's gravity it began to slow down. By the time it crossed the point at which the Moon's gravity became dominant it was not going anywhere near 25,000mph. From that point on it accelerated again as the Moon pulled it in.

So the straightforward equation in your question does not work because the speed was not constant during the journey.

Oh, and one lunar orbit took about 2 ours, actually longer than Earth orbit, due to the lower orbital speed for lunar orbit.

More information:

http://www.universetoday.com/13562/how-long-does-it-take-to-get-to-the-moon/