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

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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