11 - 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?
 

08 - Sound of Impact be Heard Before the Report of the Gun Jhun Vert Fri, 04/17/2020 - 07:01 pm

Problem
A bullet is fired at a target 1,342 m away. At what point along its path would the sound of the impact of the bullet be heard 1/4 second before the report of the gun, assuming that sound travels at the rate of 335 m/sec and the bullet is 503 m/sec.
 

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?