Horse friends - math puzzle
Three horses are standing in a triangular field, which is exactly 100 yards on each side. One horse stands at each corner; and simultaneously all three set off running. Each horse runs after the horse in the adjacent corner on his left, thus following a curved course, which terminates in the middle of the field, all three horses arriving there together. The horses obviously ran at the same speed, but just how far did they run?
Exactly 100 yards. This is because at any moment the horses are at the vertices of an equilateral triangle which diminishes at the velocity of the horses. Thus 100/V is the time it takes for the triangle to become a point in the middle of the field. The distance the horses travel during that time is V x 100/V which equals exactly 100 yards.