It is about 490 miles, but would not necessarily be the fastest route due to the quality of roads.
the shortest air route is a great circle
The shortest distance is via Fort Worth and Amarillo using Interstate 45 and US 287, however the fastest route uses Interstate 35 North and Interstate 70 West.
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The route with the shortest driving time is about 360 miles.
The shortest route between Salt Lake City and Denver is typically via I-80 E and I-25 S. This route stretches approximately 600 miles and takes around 8 to 9 hours of driving time, depending on traffic and road conditions. Travelers may also consider I-70 E, which offers scenic views but can be slightly longer. Always check for current road conditions and closures before starting your journey.
The shortest route between two points on the surface of a planet, when routes are limited to the planet's surface, is the arc of the great circle that connects the two points. The shortest route between two points anywhere, without regard to intervening matter or energy preventing the route from being followed, is always the line connecting the two points.
Great Circle Route
The city closest to Denver, Colorado, via interstate highways is Colorado Springs. It is approximately 70 miles south of Denver, accessible primarily via Interstate 25. This route offers a direct and efficient drive between the two cities.
Take I-84 EAST to I-80 EAST to CHEYENNE in Utah.Take I-80 EAST to I-25 SOUTH to DENVER at EXIT 359A in Wyoming near Cheyenne.Take I-25 SOUTH to Denver.
The fastest shortest path algorithm for finding the most efficient route between two points is Dijkstra's algorithm.
straight line