The faster you walk, the quicker you'll get there, it's true. But be warned, it's not without a price, for the faster you go, the further you'll have to walk before you arrive.
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$\begingroup$ Does this has anything to do with the space-time relativity paradox? $\endgroup$– prog_SAHILJan 2 '18 at 15:38
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This could work:
You're meeting a friend walking towards you (replace friend by anything that travels in your direction : bus, train etc...). The faster you go, the further you'll meet him, albeit quicker.
Alternatively (with the same reasoning):
You're walking on a conveying belt.
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$\begingroup$ You're on the right track, but it's not the scenario that prompted this riddle. $\endgroup$ Jan 2 '18 at 15:29
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2$\begingroup$ The first scenario perfectly fits every part of the puzzle. If it isn’t acceptable as an answer, the question may be overly broad. $\endgroup$– BassJan 2 '18 at 16:41
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$\begingroup$ Accepting the second solution. This notion came to me while I was on a moving walkway at the airport. $\endgroup$ Jan 2 '18 at 19:36
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Could your destination be...
a new year/new day?
If you walk faster...
towards the East, you will technically see the sun rise sooner on a new day/year/arbitrary increment of time. However, the faster you walk the more distance you will cover before it reaches that time.
