How to travel from Denver to Rapid City SD Mt Rushmore. Closest point by rail them by rental car?

Amtrak passenger trains run from Denver, Colorado to Rapid City, South Dakota. There are four trains a week that travel that distance. By rental car, use I-270, I-25, U.S. 20, U.S. 18, S.D. 79, then U.S. 16. Travel north or east with a distance of about 400 miles. Train will take over 10 hours. Rental car will be about 7 hours.