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You are just walking over a bridge. You have 3/8 of the bridge behind you, 5/8 ahead. Suddenly you hear a train approaching from behind (the 3/8 end), but it´s not yet on the bridge.

You know that you can turn around and run the shorter distance towards the train, or keep direction and run the longer distance. Either way, you would make it off the bridge just in time.

You run at 10 kph (or whatever velocity unit you prefer). How fast is the train?

Hint:

If you need a calculator, you are overthinking this.

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  • $\begingroup$ it seems like a question of kinematics ... $\endgroup$
    – manshu
    Mar 9, 2016 at 20:01
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    $\begingroup$ Frankly I'm not sure what kinematics mean. If that helps, the math involved is actually trivial and can be solved by 6th-graders. $\endgroup$
    – Zsolt Szilagy
    Mar 9, 2016 at 20:03
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    $\begingroup$ For the off-topic-flag: The question is not about a calculation. It is about finding the missing information in the text. $\endgroup$
    – Zsolt Szilagy
    Mar 9, 2016 at 23:35

3 Answers 3

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At the start you do not know the distance of the train to the bridge, but if you run towards the short end, you will cover 3/8 of the length of the bridge in the time it takes the train to get to the start of the bridge. If you ran the other way, you would also cover 3/8 of the length bridge when the train gets to the start of the bridge. This means you are 3/8+3/8 along on the bridge when the train gets to the start. You then can cover the remaining 1/4 of the bridge in the time it takes the train to cover the entire bridge.

Therefore

The train is moving 4x as fast as you (i.e., 40 kph)

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the train is travelling at 40kph

reasoning:

Since the train travels the entire bridge in the same amount of time you travel a quarter of it, it is travelling at four times your speed.

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    $\begingroup$ no I didn't. 5/8 - 3/8 = 1/4 $\endgroup$
    – Slepz
    Mar 9, 2016 at 20:14
  • $\begingroup$ you have to cover 5d/8 or 3d/8 distance if you need to get off the bridge...not 1d/4 $\endgroup$
    – manshu
    Mar 9, 2016 at 20:22
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    $\begingroup$ You might want to throw this comment (actually, throw in the explanation of the comment) in the answer - "1/4" seems out-of-nowhere on its own. $\endgroup$
    – question_asker
    Mar 9, 2016 at 20:22
  • $\begingroup$ Upvoted for the right answer. The accepted answer had more in-depth explanation. $\endgroup$
    – Zsolt Szilagy
    Mar 9, 2016 at 21:01
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You run at 10 kph (or whatever velocity unit you prefer).

I choose $10 c$ where $c$ is the velocity of light!!!
I've now entered another dimension and piddly sluggish trains don't bother me in the slightest.
I can get to places before any current event occurs in time-space.
I simply go back in time to when this approaching train was built and redesign the "cow plow" to gently scoop me up into a waiting (my new design) comfy sofa.
Then zap back and await a ready transport across the bridge.
No fuss at all.

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    $\begingroup$ I started to doubt if you can get that fast, but the 3rd exclamation mark convinced me. $\endgroup$
    – Zsolt Szilagy
    Mar 9, 2016 at 21:36
  • $\begingroup$ @Zsolt Yes, the triple-banger gets them all :) ) $\endgroup$
    – Paul Evans
    Mar 9, 2016 at 21:40
  • $\begingroup$ Maybe I am missing something, but how fast is the train going? $\endgroup$
    – StrongBad
    Mar 9, 2016 at 21:41
  • $\begingroup$ @StrongBad Hmmm, have to do some tensor analysis on that baby but I'm pretty sure once we bust relativity we don't worry about stuff like that. Maybe I should have a hospitality suite built around the sofa... with free WiFi and a massive flat screen! $\endgroup$
    – Paul Evans
    Mar 9, 2016 at 22:04

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