14 Days?

4 days in Vegas = 10 days driving.

3380 miles to AK / 10 days = 338 miles a day.

338 miles a day / 65 miles per hour = 5.2 hours of driving per day.

5 hours of driving = 19 hours of not driving

19 hours of not driving - 8 hours of sleep = 11 hours of free time


So approximately...

50 hours of driving
110 hours of free time
80 hours of sleeping