Presuming no ocean currents and no change in wind speed or direction during daylight hours and no clouds....
You're off the East Coast of N America.
You get up and set sail as soon as you can discern the rising sun. You follow the sun until you can no longer see it.
Other than maybe being a tad further south than where you started, where are you?
This guy started in Miami eh? Well, maybe he satrted out south or southeast out of port and after a while if he got lost he figured if he sailed west he wouldn't hit land until he hit Mexico or Texas by way of the Gulf. Maybe he split the difference and sailed north and ended up where he did.