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Horse carriage

Horse carriage

This is one of those curious and instructive riddles that can occur to us while we take a morning walk and that is able to feed our reflections even in the afternoon.

Recently, while walking with a friend in the country, we met his son who passed in a car pulled by a pony at high speed, taking a curve so close that he almost put the car upside down and his father's nerves.

In the discussion that followed later, when we got home, there was such a disparity of opinions between father and son about the world of traction, speed, turns and their relationship with the concept of overturning, that we did a practical experiment of which This riddle was born:

The drawing will help, not only to explain the nature of the puzzle, but to rely on common sense and intuition when solving it, without pulling both figures and calculation rules of concentric circles.

By rotating the car within a ring of a certain diameter that we can establish as reasonably safe, it was found that the outer wheels rotated twice for each turn of the internal ones and that the wheels were separated by the usual distance of the 5-foot axle.

The problem is to find out the circumference of the path marked by the outer wheels when turning.

Solution

For the outer wheel to go twice as fast as the inner wheel, the circumference of that wheel must be twice as large as that of the other. As five feet equals half the radius of the outer wheel, the radius would be 10 feet, and the diameter of 20 feet.

3.1416 times 20 feet gives us 62,832, which is the circumference of the circle described by the outer wheel.