Missing Time

One morning you awake to find that the only clock in the house has ceased to work. On closer inspection, you discover that this clock is of the mechanical pendulum variety, and someone simply forgot to set the gravity pull system. With a quick pull, you reset it in motion, and it begins ticking again.

You then suddenly realize that today is the annual puzzler's convention, and you're the keynote speaker. Quickly grabbing your hat and cane, you begin briskly strolling toward the convention hall in the town center, at a steady and deliberate pace.

Halfway there, you glance up and see from the town clock that there is quite a bit of time to spare. Slowing to a more leisurely pace, you arrive in plenty of time to give what will later be considered to be the definitive lecture on the monty hall problem.

Halfway home, you glance up at the clock and notice it is getting rather late. You accelerate back to briskly strolling, arrive home, drop off your hat and cane, and then set the clock, now to the correct time.

You didn't know how far or long the walk to the convention hall was, nor do you know your speed. All you know is that: a) your "briskly strolling" pace is a constant velocity and b) your leisurely pace is not.

How did you know the correct time when you returned?