You want to get from one end of an airport terminal to the other, but you must tie up your shoelace on the way. Is it quicker to tie your shoelace when you are on a moving walkway or when you are on stationary ground? (I borrowed the problem from Terry Tao’s blog.)
Deniz Yukselir won the prize, with a clever graphical solution.
Terry Tao discusses the problem and some extensions on this web page.
In algebra: if you walk at speed v, and the walkway moves at speed u, and it takes time t to tie your laces, then the person who ties her or his shoelaces off-walkway falls (v+u)t behind the person on the walkway, and only catches up by vt when the other person stops on the walkway to tie her or his laces.
Therefore, it’s best to tie your laces on the walkway.