What is the average mph a commerial truck driver can drive legally in a day?

That depends on what state they're driving in. Some states (such as California) are especially stringent about a driver's logbook showing a lower average speed than the speed limit. Others, not so much. In a state where the terrain is relatively flat, you'll tend to have a higher average speed than a state which has lots of hills or mountains.

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Average MPH? There really isn't a "legal" average MPH.

Say you're hauling Budweiser. If you haul it out of Columbus, Ohio, your average MPH is going to be higher than if you haul it out of St. Louis because the place you pick it up from in St. Louis is farther from the Interstate than the place you pick it up from in Columbus. More city driving equals a lower average MPH.

You can legally drive 11 hours in a 14-hour period every day. How fast you go depends on where you are.