Dante's Infernal Puzzle Collection -- 12. Spericolato

In the amount of time it took the horse rider to vanish around the turn, the man walked 52 paces.

Also note that it took the man 52 + 312 = 364 paces to cover the same distance.

d = the distance from the point of their encounter to the turn

t = the time it took for the horse rider to vanish around the turn = the time it took the man to walk 52 paces

Note that it took the man (364/52) * t to reach the circle.

Since [speed = distance / time], the speed of the horse rider is d/t, whereas the speed of the man is d/(364/52)t.

Since the man claims that his speed is 2 leagues per hour, we can set up the problem as follows:

d/(364/52)t : 2 = d/t : x, where x is the horse rider's speed.

2 * (d/t) = xd/(364/52)t

2d = xd/(364/52)

2d = (52xd)/364

2 = 52x/364

52x = 728

x = 14

Thus, the horse rider's speed is 14 leagues per hour.

Answer: 14 leagues/hr