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.
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.
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.