Puzzle time - Loose laces at the airport
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This one should be pretty accessible to a general audience.
You are walking to your gate at O'Hare and need to tie your shoelace. Up ahead is a moving walkway that you plan to use. To minimize your time to reach the gate, should you stop and tie your shoelace now, or wait and tie it on the walkway?
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I assume that if you go on the moving walkway, you will continue to walk at the same speed + the speed of the moving sidewalk, correct?
(Side topic #1. There was a study done about moving sidewalks in airports, and they found out that the average speed of people decreased when they were installed because people actually stood on them and didn’t continue moving. And the walkway is moved at a slower pace than the average person.)
(Side topic #2. When I was flying a lot between Far East and US, I would usually fly out of terminal 1, Concourse C. at Ohare airport. You have to walk through the underground area to get there and there are 4 sets x 2 of moving walkways in that underground passage. It Amazed me that probably 90% of the time I was there, at least one of them of the eight was out of service! A Different one each time, but always at least one was broken. )
(Side tropic #3. United airlines had a promotion for a while where they would take people who flew a lot, and would have a Mercedes vehicle drive you from the lounge directly to the jetway of your plane. You walked outside the lounge, got in a Mercedes car, and they drove you. And then they would hand you a card that gave you some type of discount on a new Mercedes. It was fun to do, but I think it actually took longer, then to just walk there to the gate. :-). )
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I’ve studied informally people who just stop walking on walkways and then block passage. It’s fascinating and unflattering look at Americana. Some airports such as O’Hare seem to rely on them less... I just know there it’s on foot most the time.
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I assume there's a general answer to the question other than "it doesn't matter", only because the speed of the walkway as compared to the walking speed are not specified and don't matter. Neither is how long tying the shoes take as compared to time on the walkway specified, so that can't matter either. Given a reductio of the time to tie shoes equalling the time it takes for the walkway to move its whole distance, i.e. starting to tie the shoes as soon as your on the walkway and finishing when the walkway is done, the answer to that question is that you should tie them on the walkway. So this specific can probably be safely generalized. I think it has to do with extending time on the walkway. Time spent tying shoes off the walkway is truly wasted.
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@Loki said in Puzzle time - Loose laces at the airport:
I once had a guy warn me that if I passed him he would break my face. I said I am sorry sir and put my head down. Never mess with an insane person.
Larry made you call him sir?!
That is unusual.
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Related puzzle:
You've just poured yourself a cup of coffee and were just about to add milk when you noticed you had to do something urgently for 5min before you can drink the coffee.
If you want to maximize the temperature of the coffee when you finally drink it, should you add the (cool) milk now or just before drinking?
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@Klaus said in Puzzle time - Loose laces at the airport:
Related puzzle:
You've just poured yourself a cup of coffee and were just about to add milk when you noticed you had to do something urgently for 5min before you can drink the coffee.
If you want to maximize the temperature of the coffee when you finally drink it, should you add the (cool) milk now or just before drinking?
Just make sure to tie your shoelaces before u run off to the bathroom (or something otherwise urgent) or you will trip and spill the hot coffee on your pants and end up getting a second degree burn on the dong, which will make your plane trip out of ohare very uncomfortable.
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@Klaus said in Puzzle time - Loose laces at the airport:
Related puzzle:
You've just poured yourself a cup of coffee and were just about to add milk when you noticed you had to do something urgently for 5min before you can drink the coffee.
If you want to maximize the temperature of the coffee when you finally drink it, should you add the (cool) milk now or just before drinking?
Depends on how cold the milk is relative to ambient temperature. If the milk is already at or close to ambient temperature, add the milk now. Strategy is to take advanced of the fact that heat transfers at a slower rate when coffee is closer to ambient temperature.
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I never circled back here.
Horace is right, tie them on the walkway.
For an intuitive answer, imagine walking with your friend together. Right when you get up to the walkway, but before you step on, you stop to tie your shoes. Your friend takes that one extra step and ties them on the walkway. 10 seconds later (say) you both finish and start walking again at the same speed. You’ll never catch up.
Interestingly, this problem came from Terrance Tao.
https://terrytao.wordpress.com/2008/12/09/an-airport-inspired-puzzle/
Best comment:
I asked myself exactly the same questions the first time I was in an airport, namely when I was 15. So, once in my life, I can say I have investigated and solved a mathematical problem in which Terence Tao was also interested, before he did
DON’T let them eat cake.
- RFK Jr -
@jon-nyc That makes sense, but if you tie your shoe, you will finish before your friend.
(Even so, I do understand why you would not catch up)
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Because the two people basically start and stop tying their shoes at the same time (a fraction of a second apart). But in the interim the guy who stopped on the moving walkway was moved along during the time they both tied their shoes. Therefore when they start back up again (at essentially the same time) there’s a gap between them. It never closes because at this point they’re both on the walkway and both walking the same speed
DON’T let them eat cake.
- RFK Jr
