Horses to Qi

Now a good horse and an inferior horse set out from Chang’an to Qi.  Qi is 3000 li from Chang’an.  The good horse travels 193 li on the first day and daily increases by 13 li; the inferior horse travels 97 li on the first day and daily decreases by 1/2 li.  The good horse reaches Qi first and turns back to meet the inferior horse.  Tell: how many days until they meet and how far has each traveled? 

Jiuzhang Suanshu (The Nine Chapters on the Mathematical Art), c. 100 BCE

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