Average Speed

Explanations

At first sight the temptation for the most “obvious“ answer is 8 miles per hour (half of 12 + 4). But while calculating an average speed, individual speeds can not be operated on that basis. Instead, all calculations must be adapted to the distance-divided-by-time scheme.

As a result, if the whole route is considered as 1, the first half is taken by the horse in 1/2 / 12 = 1/24 unit of time. The second half is taken in 1/2 / 4 = 1/8 unit of time. The sum of both times (in contrast to the speeds, individual times can be added validly) is 1/24 + 1/8 = 4/24 = 1/6 unit of time.

Dividing the entire route of 1 by the total travel time of 1/6, we get: 1 / 1/6 = 6 miles per hour as the horse's average speed for the entire route.

[After Boris A. Kordemsky. The Moscow Puzzles: 359 mathematical recreations. 1972]