You have just managed to catch up to your friend in a race, on a road which goes on forever in both directions. Your friend is a bad loser, and full of adrenaline from the race. "Try and catch me this time", your friend says, and knocks you out cold. When you recover, you have no idea how much time has passed.

You move at constant speed x>1 m/s and your friend moves at constant speed 1 m/s.

Visibility is limited so you will not be able to see your friend from a distance.

You must not stray from the road, same goes for your friend.

Can you catch up to your friend? Does the answer depend on your speed x, and if so, what is the minimum x for which you can catch up? What is your strategy?

This is a sequel to the puzzle:

You have just managed to catch up to your friend in a race, on a road which goes on forever in both directions. Your friend is a bad loser, and full of adrenaline from the race. "Try and catch me this time", your friend says, and knocks you out cold. When you recover, you have no idea how much time has passed.

Can you catch up to your friend? Does the answer depend on your speed x, and if so, what is the minimum x for which you can catch up? What is your strategy?

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