Here is a general overview of the route:
1. Drumheller, Alberta to Lethbridge, Alberta: Approximately 2.5 hours (175 miles).
2. Lethbridge, Alberta to Great Falls, Montana: Approximately 3 hours (210 miles).
3. Great Falls, Montana to Billings, Montana: Approximately 2 hours (165 miles).
4. Billings, Montana to Cody, Wyoming: Approximately 2.5 hours (160 miles).
5. Cody, Wyoming to Jackson Hole, Wyoming: Approximately 2 hours (105 miles).
6. Jackson Hole, Wyoming to West Yellowstone, Montana: Approximately 1.5 hours (60 miles).
7. West Yellowstone, Montana to Idaho Falls, Idaho: Approximately 2 hours (125 miles).
8. Idaho Falls, Idaho to Salt Lake City, Utah: Approximately 3.5 hours (220 miles).
9. Salt Lake City, Utah to Las Vegas, Nevada: Approximately 6.5 hours (435 miles).
Please note that these driving times are approximate and may vary depending on various factors such as traffic, weather conditions, and road construction. It is recommended to check the latest road conditions and plan accordingly.