Based on review of this clip, Aragorn hears the horn of Boromir and immediately begins running towards the sound (about 0:11 of the clip). One orc gets in his way, and he whacks it dead, an interaction that takes about 3 or 4 seconds.
Boromir takes at least a couple of minutes to die (he is still alive when Merry and Pippin are taken at 2:40); it doesn't appear that Aragorn's delay of a few seconds to kill the orc makes any difference to his time of arrival. Given that he started as soon as the horn blew, I conclude that he came as soon as he was aware there was a problem, and this was not soon enough for him to prevent Boromir's death.
In the book, Aragorn runs up the hill to the Seat of Seeing at the summit. He is at this point unaware that there is an attack going on, though he has forecast that one is likely. He runs back down the hill towards the sound as quickly as he can:
Even as he gazed his quick ears caught sounds in the woodlands below, on the west side of the River. He stiffened. There were cries, and among them, to his horror, he could distinguish the harsh voices of Orcs. Then suddenly with a deep-throated call a great horn blew, and the blasts of it smote the hills and echoed in the hollows, rising in a mighty shout above the roaring of the falls.
'The horn of Boromir!' he cried. 'He is in need!' He sprang down the steps and away, leaping down the path. 'Alas! An ill fate is on me this day, and all that I do goes amiss. Where is Sam?'
As he ran the cries came louder, but fainter now and desperately the horn was blowing. Fierce and shrill rose the yells of the Orcs, and suddenly the horn-calls ceased. Aragorn raced down the last slope, but before he could reach the hill's foot, the sounds died away; and as he turned to the left and ran towards them they retreated, until at last he could hear them no more. Drawing his bright sword and crying Elendil! Elendil! he crashed through the trees.
In this narration Legolas and Gimli are not with Aragorn; he has gone off up the hill with only Sam, and Legolas and Gimli have been fighting the orcs on "the western slopes of the hill".
Again, then, we see Aragorn unaware that Boromir is in trouble until the horn blows, and running as fast as he can to assist as soon as he does hear the horn. And again, he came as soon as he was aware there was a problem, and this was not soon enough for him to prevent Boromir's death.
(all quotation from The Lord of the Rings, Book III, Chapter 1, "The Departure of Boromir")