The fair place to meet is Denver, CO — the city closest to the midpoint of Memphis and Salt Lake City. From the farther side that’s about 18 hr 24 min of driving.
Recommended midpoint
Denver, CO
From Memphis
18 hr 24 min
877 mi to Denver
From Salt Lake City
7 hr 46 min
371 mi to Denver
Salt Lake City has the shorter trip; the split is off by about 10 hr 38 min. The alternatives below can even it out. Memphis and Salt Lake City are about 1,248 miles apart.
Memphis and Salt Lake City are about 1,248 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 18 hr 24 min of driving on the Memphis side and 7 hr 46 min on the Salt Lake City side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Denver still makes a fair, central place for Memphis and Salt Lake City to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Oklahoma City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Memphis and Salt Lake City.
Denver is the capital and most populous city of the U.S. state of Colorado. Officially a consolidated city and county, it is located in the South Platte River valley on the western edge of the High Plains, and is just east of the Front Range of the Rocky… Read more →
Memphis is a city in Shelby County, Tennessee, United States, and its county seat. Read more →
Salt Lake City, often shortened to Salt Lake or SLC, is the capital and most populous city of the U.S. state of Utah. It is the county seat of Salt Lake County, the most populous county in the state. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.