Moving walkway puzzle

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ceptimus
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Moving walkway puzzle

Post by ceptimus »

At an airport you're trying to walk to the gate before it closes. Part of your journey is regular walking along corridors and part on moving walkways. You need to briefly stop walking somewhere along the way (say to tie your shoelace?). Is it better to stop walking in the corridor or on the walkway, or doesn't it make any difference?
ed
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Re: Moving walkway puzzle

Post by ed »

Walkway. You are still moving.

Where are you going anyway? Are your papers in order? Who gave you permission to leave? What are you running from? Why do you have shoelaces? Are you mocking people with arthritis? You think not being able to tie shoelaces because you are a fat bastard is funny? You think I'm funny? What the fuck are you looking at? I'm done with you. Welcome to ignore. :x
Anaxagoras
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Re: Moving walkway puzzle

Post by Anaxagoras »

ceptimus wrote:At an airport you're trying to walk to the gate before it closes. Part of your journey is regular walking along corridors and part on moving walkways. You need to briefly stop walking somewhere along the way (say to tie your shoelace?). Is it better to stop walking in the corridor or on the walkway, or doesn't it make any difference?
Can you walk faster after you tie your shoes? If so, do it as soon as possible. I walk on the walkways of course. I use them to add speed, not to just stand there and wait.
Rob Lister
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Re: Moving walkway puzzle

Post by Rob Lister »

corridor. Because you can also walk on a walkway, you're walking twice as fast. Stopping briefly in the corridor does not lose you as much distance.
Pyrrho
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Re: Moving walkway puzzle

Post by Pyrrho »

In terms of distance covered, Lister's answer.

In terms of safety, the corridor, because then you are less likely to be rear-ended by folks who are waking twice as fast in the high-speed lane on the moving walkway. And yes, there is a high-speed lane. People act as if they're driving. Folks who just stand on the walkway on the right, speedsters fast-walking on the left.

However, if you stop to tie your loafers in the corridor, ed's answer.
Mentat
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Re: Moving walkway puzzle

Post by Mentat »

Moving Walkway. If you stop in the corridor, you're stopped for some period of time, and that's added to the total time. But if you stop on the walkway, less than the period of time to tie the shoes is added, because you still remove the additional time due to using the conveyor passively. Or more algebraically: The increase of travel time is the shoe period time multiplied by the ratio of walking speed to walking + conveyor speed. Since that last factor is a fraction less than one, it's smaller than the time it takes to tie your shoes.
Mentat
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Re: Moving walkway puzzle

Post by Mentat »

Algebra: Let n be the distance of the corridor, m be the distance of the walkway, a be walking speed, and b be the conveyor speed. Let s be the time it takes to tie your shoes

Without stopping, the unencumbered time to destination is T = (n/a) + (m/(a+b))
Stopping in the corridor: time = (n/a) + s + (m/(a+b)) = T + s
Stopping in the walkway: First, let d be the distance covered on the walkway when you stop to tie your shoes. So m is broken up into two segments: distance d covered, and the remaining m-d of regular walking. Assume d<=m to make the math easier; the logic holds even if d>m.
So d = speed of walkway * duration of shoeing your tie = b * s
time = (n/a) + (d/b) + ((m-d)/(a+b))
= (n/a) + (b*s/b) + ((m-b*s)/(a+b))
= (n/a) + ((m-b*s)/(a+b)) + s
= (n/a) + (m/(a+b)) + s - (b*s/(a+b))
= T + s - (b*s/(a+b))
= T + s * (1 - (b/(a+b))
= T + s * a /(a+b)
< T + s

since 0 < a/(a+b) < 1
gnome
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Re: Moving walkway puzzle

Post by gnome »

If you're in such a hurry, take off the shoes and continue. You have to take them off at the security gate anyway.
ceptimus
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Re: Moving walkway puzzle

Post by ceptimus »

Pyrrho wrote:In terms of distance covered, Lister's answer.

In terms of safety, the corridor, because then you are less likely to be rear-ended by folks who are waking twice as fast in the high-speed lane on the moving walkway. And yes, there is a high-speed lane. People act as if they're driving. Folks who just stand on the walkway on the right, speedsters fast-walking on the left.

However, if you stop to tie your loafers in the corridor, ed's answer.
People walking versus people standing on the moving walkway only have the same relative speed as people walking versus people standing in the corridor. The only reason that you'd be more likely to be rear-ended on the walkway is that it's narrower.
Anaxagoras
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Re: Moving walkway puzzle

Post by Anaxagoras »

If you don't tie your shoes, the loose laces could be caught in the moving walkway. Or it could cause you to trip. Besides, you look stupid walking around with an untied shoe, and the laces will get frayed. If your shoes need tying, generally best to do it asap.

Mathematically, it's a wash anyway.
Witness
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Re: Moving walkway puzzle

Post by Witness »

What Mentat wrote. I'll give you anyway what I came up with:


Let's call T the delay (for tying the shoelaces).

We can neglect stopping in a corridor as it just adds T to the travel time.

On a walkway we have to consider the speeds:
v of the pedestrian
w of the walkway

And the length d of the walkway.

If there is no stop (on the walkway), the speeds add and the walkway is crossed in T0 = d/(v + w)

With a stop the pedestrian is carried along a distance wT (during time T) at speed w, and the remaining distance d – wT at speed v + w.

The travel time (on the walkway) becomes:
T + (d – wT)/(v + w) =
T + d/(v+w) – T*w/(v + w) =
d/(v + w) + T(1 – w/(v + w)) =
T0 + T*(v + w – w)/(v + w) =
T0 + T*v/(v + w) <
T0 + T as v/(v + w) < 1.

The shoelacing delay gets "shortened" in total travel time in the ratio (speed of pedestrian)/(sum of speeds pedestrian + walkway).


A more intuitive way would be to consider a very fast walkway: walking or being carried along would only make a negligible difference.


Now ditto with relativistic speeds for both. :mrgreen: