I cannot stop loving the book A Moscow Math Circle – Week by week problem sets by Sergey Dorinchenko. So here is another one from this great collection.
Anisha and Arushi are riding down an escalator. Halfway down the escalator, Arushi grabbed Anisha’s hat and threw it on the up escalator (and such things often happen!). Anisha ran up the down escalator in order to run down the up escalator after her hat. Arushi ran down the down escalator in order to run up the up escalator after the hat. Who will be the first to the hat? Assume the speeds of the girls relative to the escalator are equal and do not depend on the direction of motion.
As always, please send your answers as comments within the blog (preferred), or send an e-mail to firstname.lastname@example.org. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.