2008-02-16

The Hourglasses

Bengt is visiting his grandmother, who lives in a very small and very old-fashioned village far out in the countryside. The village is so old-fashioned that there are no mechanical or electric clocks, only hourglasses.
In every house is an hourglass. Every whole hour the sand runs out in all of them, and the villagers instantly turn them.
But Bengt's grandmother is very very old, and now she has forgot to turn it. Bengt has to fix this by going to one of the neighbours to look at their hourglass. The problem is that one can only read the time when the hourglass is being turned, and the hourglasses are mounted on walls so you can't carry them away.
Bengt can walk with perfectly constant speed, and it takes only a few minutes to get to the nearest neighbour. He doesn't know exactly how fast he walks or how far it is, but he does know that there is a well at exactly half the distance.
    How should Bengt go about making granny's hourglass catch up with the rest of the village? (Shouting is not allowed.)