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Two Men Meet
A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city. One walks out the south gate, the other the east gate. The person walking south proceeds an unknown number of pu then turns northeast and continues past the corner of the city until they meet the eastward traveler. The ratio of the speeds for the southward and eastward travelers is 5:3. How many pu did each walk before they met? [1 li= 300 pu]
Jiuzhang Suanshu (The Nine Chapters on the Mathematical Art), c. 100 BCE
Click here to reveal the answer
The answer is: the person traveling south proceeds 2300 pu from the center of the city, then continues \(4887\dfrac{1}{2}\) pu northeastward to meet the eastward traveler who has proceeded \(4312\dfrac{1}{2}\) pu from the center of the city
"Two Men Meet," Convergence (July 2006)
