During the Giantachomy potrayed in the story of Hercules, Hercules defeats the Giant Alkyoneus by dragging him outside of Greece:
http://www.perseus.tufts.edu/Herakles/giants.html
“Soon Alkyoneus began to revive. But before he woke up completely, Athena told Hercules that Alkyoneus would not die unless he was outside of his birthplace, in Thrace. So Hercules dragged Alkyoneus far away, and there he died.”
In terms of distance Mount Olympus is in Greece today and this is where Thrace was at the time of it’s existence:
Judging from the marked area on the first map, you would have to reach at least the area of what appears to be modern Topeiros to be in Thrace.
Google Earths says the hike’s about 326 kms so this will the distance.
In terms of timeframe it’s hard to say but based on the Context of the story Hercules had to have accomplished this promptly since he returned to aid the Gods before the battle was over.
”Meanwhile, Porphyrion had reached the top of Olympus. He had Hera cornered between the rocks and the sheer cliff. When Porphyrion began to attack the goddess, Hera called for help. Zeus cast his thunderbolt at Porphyrion, leaving him dazed, and Hercules, who had just rejoined the battle, shot him dead with an arrow. Now all the gods and Giants entered the fight. Apollo shot one of the Giants in the right eye, and Hercules shot him in the left eye. Dionysos killed one by whacking him with his thyrsus, or staff. Hecate set another Giant on fire with torches. Hephaistos eliminated one by pelting him with white-hot metal.”
Now even though Im certain this is a somewhat abridged version of the story, the specific details regarding the distance Herc traveled to kill Alkyoneus, and his return the battle shortly after do not change.
So for timeframe I’ll be conservative and say it had to have least taken place over minutes not hours, considering the battle escalated with each Giant’s arrival at the peak of Olympus so Herc couldn’t have been far away for long.
Herc also traveled there and back so 652 km
Low End: 30 Minutes 652000/1,800 = 362.22 m/s, Just over Mach 1, Supersonic
Mid-End: 10 Minutes 652000/600 = 1,086.6 m/s, Mach 3.1, Supersonic+
High-End: 5 Minutes 652000/300 = 2,173.3 m/s, Mach 6.2, Hypersonic
Whaddya think? Legit or naw.