Zhang Qiujian Suanjing/Examples/Example 1

Example of Problem from by

 * A man, who had stolen a horse, rode away on its back.
 * When he had gone $37$ miles, the owner discovered the theft and pursued the thief for $145$ miles;
 * then he returned, believing himself unable to overtake him.
 * When he turned back, the thief was riding $23$ miles ahead of him;
 * if he had continued the pursuit without coming back, in how many further miles would he have overtaken him?

Solution

 * $238 \dfrac {3} {14}$ miles.

Proof
The pursuer gains $37 - 23 = 14$ miles in $145$ miles.

So he will catch up $37$ miles in $145 \times \dfrac {37} {14}$ miles.

Thus the extra distance needed to travel is:
 * $145 \times \dfrac {37} {14} - 145 = 238 \dfrac {3} {14}$ miles.