I moved to Colorado Springs from Garner in 2010. Had I driven straight through, Google Maps gave me an estimate of 26 hours and change driving time. You can expect about the same going from Raleigh to Denver.
185 miles taking this route: Take I-40 WEST from Raleigh to NC-16 to NEWTON - CONOVER and TAYLORSVILLE at EXIT 132. Turn left off the exit ramp onto NC-16 SOUTH to NEWTON - CONOVER; take NC-16 SOUTH to Denver.
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