A Halloween Puzzle I found!

Main Question or Discussion Point

I found this little puzzle on Reddit a couple minutes ago: Puzzle Here

I worked out the first half, but need to try the second part of "How fast a monster can we out run?".

It's an entertaining puzzle, if you'd like to give it a try, don't scroll down, it gives the solutions!

Related General Discussion News on Phys.org
mfb
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Bonus question: what happens with two monsters, starting on opposite sides of the lake?
I think the best solution is better than the trivial lower bound on the maximal monster speed, but the ideal monster patterns get complicated.

or you could be a particle and not let the monster know both where you are and how fast you are going thus making it impossible for him to catch you

jmneutr0nn3
Bonus question: what happens with two monsters, starting on opposite sides of the lake?
I think the best solution is better than the trivial lower bound on the maximal monster speed, but the ideal monster patterns get complicated.

I'd like to see the answer to this bonus question. This is an impossible situation and I think the escape plan is difficult.