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Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 3, May 2014

Riddle e-news
How long is the total route travelled by the dove?

There are two cyclists, one at either end of a 20 km (12.5 miles) road. They start at the same time and meet halfway down the road. They are travelling at 10 km/h (6.25 mph).

At the same time as the cyclists depart, a dove starts at one end of the road and flies towards the second cyclist at a speed of 20 km/h (12.5 mph). When the dove reaches the first cyclist, it turns immediately around and flies back towards the second cyclist, who has already completed part of the route. When it reaches the second cyclist, the dove turns back again and continues to fly back and forth between the two cyclists until they arrive at the halfway point.

How long is the total route, comprised of an undefined number of ever decreasing distances, travelled by the dove?

Solution

This could require a somewhat complicated method to calculate the distance. You can work out the solution much more easily if you consider time as the most important factor:

Both cyclists will take an hour to reach the halfway point.

The dove flies back and forth for an hour between the two cyclists until they meet. Since the dove flies at a speed of 20 km/h (12.5 mph), it covers a total distance of 20 km.