# Motions Towards Each Other

## 11 - Distance Traveled By A Messenger From Rear To Front Then Back To Rear Of A Marching Battalion

**Problem**

A battalion, 20 miles long, advances 20 miles. During this time, a messenger on a horse travels from the rear of the battalion to the front and immediately turns around, ending up precisely at the rear of the battalion upon the completion of the 20-mile journey. How far has the messenger traveled?

## 10 - Messenger Going From Front To Rear Then To Front Of A Marching Army Column

**Problem**

An army of troops is marching along a road at 5 kph. A messenger on horseback was sent from the front to the rear of the column and returns immediately back. The total time taken being 10 minutes. Assuming the messenger rides at the rate of 10 kph, determine the length of the column.