# Airport puzzler

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From Australian mathematician Terry Tao [HT: Greg Mankiw]:

Suppose you are trying to get from one end A of a terminal to the other end B. (For simplicity, assume the terminal is a one-dimensional line segment.) Some portions of the terminal have moving walkways (in both directions); other portions do not. Your walking speed is a constant v, but while on a walkway, it is boosted by the speed u of the walkway for a net speed of v+u. (Obviously, given a choice, one would only take those walkways that are going in the direction one wishes to travel in.) Your objective is to get from A to B in the shortest time possible.

1. Suppose you need to pause for some period of time, say to tie your shoe. Is it more efficient to do so while on a walkway, or off the walkway? Assume the period of time required is the same in both cases.

2. Suppose you have a limited amount of energy available to run and increase your speed to a higher quantity v’ (or v’+u, if you are on a walkway). Is it more efficient to run while on a walkway, or off the walkway? Assume that the energy expenditure is the same in both cases.

I told this one to the kids this morning where A was security and B was the plane. My 7 year old son, for 1, without hesitation answered “tie your shoe on the plane.” I guess that is the correct answer. But don’t feel bad if you are a bit slow, he has extensive experience with the untied shoe lace problem.

All of this ignores the practicalities that there are inevitably people standing still on the moving walkway and blocking the entire path. So in real life, it can be quicker to tie the shoe laces on the moving walkway while waiting for the blockage to clear!

Airports have become shopping malls – and overpriced ones at that.