Puzzle n°12 (*) - The burning vine

Once upon a time, there was a very dangerous forest.
It was dangerous because it was the home of snakes whose bite was deadly.
It was possible to survive the wound only if one could drink a specific anti-poison exactly 45 minutes after the bite.

One day, a somali attempted to cross this forest.
He had not forgotten his bottle of anti-poison, but didn't have any watch or hourglass to measure time.
Hopefully, in this forest, there were also a lot of magical vines,
which had the curious property of burning in exactly one hour when lit at either of their two ends.
However, the progression of the fire along the vine was neither regular nor predictible :
for instance, if you would cut a vine in two halves of equal length, these two halves might not take the same time to burn down.

Now our somali has been attacked by a snake... There are many vines around him and he carries a lighter to light them. But he will surely die if he can't manage to use them to measure exactly 45 minutes after the snake has bitten ! Can you help him, quick ?

... I'm giving up ...