About 3 hours and 48 minutes.
It is about 160 miles.
Florida has a Sunrise 33.08 miles north of Miami and a second Sunrise on the Gulf Coast near Saint Petersburg that is 220.90 miles from Miami, hower the Sun only rises once each day in the Sunshine...
MapQuest estimates the driving time as 4 hours and 40 minutes.
MapQuest gives the estimated driving time as 3 hours and 26 minutes.