Shoelace+problem

Here is an intriguing real world math problem that was posed by Terry Tao.

//You are walking from one end of an airport terminal to the other. The airport has several moving walkways, and you need to stop to tie your shoelace. Assuming you want to get to the other end as quickly as possible, is it better to tie your shoelace while you are on a moving walkway or while you are between walkways?//

Some of my friends who work at the airport had more practical suggestions, such as "call a cart" or "wear loafers", but I am more interested in the mathematical question. The worksheet below shows a time-distance graph for each of the two scenarios. The green line shows what happens if you tie your shoelace while you are on the moving walkway, and the red line shows what happens if you tie your shoelace while you are between walkways.


 * Conclusion:** It is quicker to tie your shoelace while you are on a moving walkway.

media type="custom" key="20990284"