Answer :

Beowulf was motived to travel across the sea to help Hrothgar because of Hrothgar's friendship with Beowulf's father. Hrothgar sent men to help Beowulf's father when he needed help, so Beowulf feels he owes a debt of allegiance to Hrothgar. 
Hrothgar was the king of Denmark and needed help in overcoming the monster Grendel. Legend had it that Beowulf had the strength of thirty men in each hand. Beowulf met with Hrothgar and offered to fight Grendel without any weapons. Hrothgar welcomed Beowulf and his companions and invited them to a feast with his Danish warriors.

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