Zhang Qiujian Suanjing/Examples/Example 1

Example of Problem from Zhang Qiujian Suanjing by Zhang Qiujian

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?

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

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.

$\blacksquare$