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About 300 miles.
2 to 3 hous if you don't stop
Given is the calculated distance as well as the driving travel time, which does not take into account driving conditions, traffic, etc. The distance between Dallas, Texas and Galveston, Texas is 291 miles. The resulting travel time is 4 hours and 56 minutes.
Using Google Maps one is able to calculate the distance as well as the driving travel time.

The distance between Dallas, Texas and Galveston, Texas is 291 miles. The travel time is 4 hours and 56 minutes.
288 mi - about 4 hours 31 mins
Approximately 290 miles or approximately 3 hours driving time.

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