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?

Your answer would be right if the messenger ran the round trip before the rest of the company began their daily march, but the problem states that he began his run at the same time as the march began, and ended it when the march ended.

Assume that he runs approximately 3 times as fast as the marchers (It's not accurate, but it is close enough to illustrate my point, and it avoids the square root -- for now). When he has gone 25 miles, he is where the lead officer started out, but the lead officer has had time to march 8 1/3 miles. He finally catches up to the lead officer at 12 1/2 miles, and turns back. He only has to go back the "extra" 12 1/2 miles to get to where he's going to spend the night, so he would run 50 miles if he were running at three times the speed of the march. But he would get there when the marchers had only gone 2/3 of their 25 miles. Going slower would mean that he would finish closer to the correct time, but it would also mean that the lead officer would have more time to go further before he caught up, so he would have run a longer distance. When the time he gets to the finish is the same as the time the other marchers finish, the distance works out to the 60+ miles I mentioned earlier.

Posted by TomM on 2002-07-08 02:27:08