All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
Marching Messenger (Posted on 2002-07-05) Difficulty: 5 of 5
(This is from CTK exchange)

A column of soldiers is 25 miles long and they march 25 miles a day. One morning a messenger started at the rear of the column with a message for the guy up front. The messenger began to march and gave the message to the guy up front and then returned to his position by the end of the day. Assume that the messenger marched at the same rate of speed the whole time. How many miles did the messenger march?

See The Solution Submitted by Dulanjana    
Rating: 4.1667 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Forced March | Comment 1 of 13
Consider three times during the march:

At T = 0, the messenger is at point A (0 miles from point A) the lead officer is at point B (25 miles from point A)

At T = t (when they meet), the lead officer is at point C (d miles from point B); the messenger is also at point C (d + 25 miles from point A.
The officer's speed was d/t. The messenger's speed was (d + 25)/t

At T = 1 days march, the officer is at point D (25 miles from point B); the messenger is at point B (d miles from point C) The officer's speed was 25/(1 day's march)

The officer marched at a steady pace, so d/t = 25 or d = 25t

The total distance covered by the messenger was 25 + 2d; the time was 1 days march; the speed was (d + 25)/t

So we have two equations:
d = 25t
25 + 2d = 1 * (d + 25)/t

Substituting for d, we get
25 + 50t = (25 + 25t)/t

25t + 50 t = 25 + 25t
50 t = 25
2t = 1
t =
t = 1 /√2

so d = 25t = 25/√2
and 2d = 2(25/√2) = 25(√2)

and the messenger travelled 25 + 2d = 25 (1 + √2), or approx 60.355 miles

  Posted by TomM on 2002-07-04 16:56:30
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (6)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information