The time it takes is irrelevant. The quality of the time it takes is memorable.
It matters not as how long that the individual or individuals that are hiking enjoy take to make this trip, but it does matter as to the multiplicity of the nature and area that they are viewing and experiencing.
This maybe not the right answer in a mathematical sense but it is in an "experiential" sense.
Jud Kastner [email protected]
The total distance from the North Rim to the Phantom Ranch is 14 miles. This can be a rough descent on the body, and an elevation change of almost 6,000 ft. There is the Cottonwood Campground at just about the halfway marker, should you choose to take the 14 mile hike in two legs. If you are experienced, the entire 14 miles should be possible in one day.
Having hiked to the bottom of the canyon myself, I would advise planning your travels in cooler months, and to take your time on the way back. 14 miles is a lot for most people, and especially in a desert climate. If you are not acclimated to the elevation, and don't have considerable hiking experience, take two days for both your descent and ascent through the canyon. Enjoy, and take lots of pictures!