6+ hrs from salt lake to ys

then you add the time between las vegas to salt lake. look it up from the map.

BTW, that is not counting the winter road condition.

I strongly suggest you to study a Road Atlas and see the distance, mountain passes etc instead of just asking questions. There is even a simplistic chart to show driving time / distance on any decent Road Atlas.
You need to know if there are mountain passes on your route, how much are the heights, the possibility of road closure in Winter time.

Further more, Yellow Stone only open partially during Winter.

I never understand how people dont look up the map to figure out the basic driving time and road condition, such as whether it is an Interstate, U.S., State, or local roads.