The flight from Detroit (DTW) to Las Vegas (LAS) takes about 3h 56m nonstop on a narrowbody airliner, covering 1,745 miles (2,808 km).
Las Vegas is 3 hours behind Detroit. You cross 3 time zones heading west. Westbound trips like this one are usually a little easier to adjust to, so plan for a day or two of jet lag.
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