If a rocket is going 17,500 mph how long will it take to go to the moon?

You are talking about an orbital transfer, which is not as simple as you might think it should be. The moon is moving about 1400 mph so in the 8 1/2 hours it takes you to get out there, the moon has moved another 11,900 miles and you need to slow down to get into an orbit when you catch up to it. It is not a simple task.