Easier Temple Geometry Problems
93
Cow a P Start b
Figure 4.1. How many days after starting out from P will the horse and cow meet?
Horse
Problem 3 The tablet on which this problem was written was hung by Hara Toyokatsu in 1829 at the Katsurahama shrine in Akigun of Hiroshima prefecture and measures 81 cm by 46 cm. The problem itself was quoted from the 1797 book Saitei Sanp¯o , or Revision of Certain Problems, by Fujita Kagen. As shown in figure 4.2, three circles A, B, and C of circumference 56 + 2/3 km, 30 + 5/7 km, and 13 + 3/4 kilometer, respectively, all pass through point P. Three horses a, b, and c start to walk around A, B, and C from P simultaneously. Horse a’s speed is 8 + 41/1,000 km per day, b’s is 6 + 123/4,000 km per day, and c’s is 4 + 41/2,000 km per day. How many days will pass before the three horses meet again at P? Answer: The horses meet again 20,000 days after they set out. The solution can be found on page 121.
a
c
P
b
Figure 4.2. How many days will pass before the horses meet again at P?