Kingdoms and Empires in East Asia (770 b.c.–a.d. 700)

“A fast horse and a slow horse set out together on the 3,000-li (900-kilometer or 563-mile) journey from Chang’an to Qi. The first day the fast horse travels 193 li, thereafter increasing its speed by 13 li each day. The slow horse covers 97 li on the first day, thereafter, reducing its speed by 0.5 li each day. After reaching Qi the fast horse starts its return journey and meets the slow horse. When does the meeting take place and how fast has each horse traveled?” The teacher sat cross-legged on the dais, looking down as his pupils struggled with the problem. Their heads were bent in concentration as they plied their ink-charged brushes and made rapid calculations on thin wooden boards. It was hard work but essential, for these young men would soon be candidates in the great state-run examinations. If they failed, they would return to their homes to make their own way in a family business or as a local town scribe. If they succeeded, the door would be open to high office in the Han Empire and a chance to play their part in governing its 58 million inhabitants . 1