Impulse engines are actually quite fast (relatively speaking). According to Memory-Alpha:
...the shuttles aboard the Enterprise-D had a maximum impulse velocity of approximately 2.5% of light speed...
We can use this as a notion as to how fast the Enterprise's maximum impulse velocity would be (presumably higher).
The speed of light is 299,792.458 kilometers / second. Multplying that by 2.5% we get 7 494.81145 kilometers per second. We divide the average distance of the Moon to the Earth by the maximum speed impulse presumably has and we can conclude that it would only take 51.2888152777 seconds, less than a minute for the Enterprise to go from the Moon to the Earth (on average).
To traverse a smaller distance would take considerably less time.
The above was calculated for a shuttlecraft aboard the Enterprise-D (more technologically advanced). Thanks to Xantec, we can get a more accurate estimation on how fast the Enterprise could traverse the distance. Assuming the Enterprise's maximum impulse drive moves at 0.8 warp speed, we can establish its velocity by the equation provided by Memory-Alpha:
0.8 cubed is 0.512. We can then use distance/velocity to obtain the time: approximately 2.504 seconds. Still definitely do-able in an hour's time.