As the crow flies, Grand Canyon Village on the South Rim and the Lodge at the North Rim are only 10 miles apart.  To drive between them, you have to travel 215 miles or about 5 hours.  Or you could hike from North Rim to South Rim down the North Kaibab Trail (elevation 8,241 ft – 14.3 miles) and up the Bright Angel Trail  (9.6 miles – elevation 6,860 ft) which is about 24 miles.  That’s a whole different kind of marathon!