# Algebra : Word Problem - Relative Speed

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A column of soldiers 25 miles long marches 25 miles a day. One morning, just as the day's march began, a messenger started at the rear of the column with a message for the man at the front of the column. During the day he marched forward, delivered the message to the first man in the column and returned to his position just as the day's march ended. How far did the messenger walk?

Please be detailed in your explanation. I need to understand the thought processes involved in solving this problem.

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##### Solution Summary

The distance is calculated based on the relative speed of two objects.

##### Solution Preview

The important in this problem is the velocity of the messenger relative to the moving column.

The speed of the column is 25 miles per day.

Let the actual speed of the messenger be x miles per day.

Then his velocity relative to the column,as he moves forward is

(x - 25). Remember that he has to move faster than the column to reach its front.

His distance relative to the ...

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