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.
 

07 - A Man Covers an Unknown Distance at Different Rates

Problem
A man covers the distance A to B in 5 hours and 30 minutes. During the second half of the distance he traveled 1/2 kilometer less per hour than during the first half. In the return trip from B to A, by traveling 1 km/hr faster than during the first half of his trip from A to B, he consumed 3-3/4 hours. Determine the distance AB.
 

06 - The Battleship Was Brought to Full Stop After 1 Hour of Voyage

Problem
A battleship started on a 500-mile voyage but was brought to full stop an hour after starting for military reasons, delaying it for full hour, after which it was ordered to proceed at a reduced velocity equivalent to 75% of its former rate. The ship arrived at its destination 3 hours and 3 quarters after scheduled time. If it was desired for the ship to arrive one hour and a quarter sooner, how far from the destination should the ship have been ordered stopped?