This is another problem from the c.100AD Chinese mathematical work, Jiǔ zhāng suàn shù (The Nine Chapters on the Mathematical Art) found at the MAA Convergence website Convergence.
“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]”
See Two Men Meet for a solution.