Two brain teasers for the summer

When driving back with my kids from the South of France (Bandol) to my native Belgium last week, we hit a combined afternoon rush hour / tourists passing traffic jam in the area of Lyon, on the so-called ‘rocade’ (for the experts, the tunnel de la Fourvière was also jammed). I told my kids that we were lucky to have that traffic jam on a highway portion where your speed is limited to 90 km/h. Usually you can drive 130 km/h on the French highways.

Way further up North, in the area of Reims/Cambrai, where everything was driving really smoothly and the kids were sleeping, I was thinking: Is it really so? Does it matter on your total travel time where you hit a traffic jam: Is losing 45 minutes on a 90 km/h section any different than losing 45 minutes on a 130 km/h section? I believe not.

This brought me back to a similar query I had some years ago:

Suppose you are at the airport and have to run from one side to the other to catch your next flight.  Half of your route is just plain ground, the other half are people movers (i.e. flat escalators).
You suddenly realise you have to tie your shoe laces.

Now, where would you do it? On plain ground or on the slowly moving people mover, and why?  Or would you proceed at a slower speed until the boarding gate?

For the sake of this mental exercise, assume you will not be run over, nor would you get sued for making somebody fall. And if you do stop, you may also ignore the time spent slowing down and getting back to your original speed.

Now, what do you think:

Does it matter where you hit a traffic jam?

Where would you tie your shoe laces? What are the parameters to take into consideration?

(Remark: If you tie your shoe laces on the people mover, you obviously lose time in a maximum speed section…)

Enjoy the summer !

P.S. Also posted on LinkedIn in April 2009: A small mathematics question: Where would [you] tie your shoe laces, and why?