Speed Distance Time question

[Londinium]

A column of soldiers a mile long is marching at constant speed. A messenger leaves his post at the rear of the column and walks to its front, where he delivers a message to his sergeant and then returns to his post. If he arrives back to exactly the position he would have found himself in had he not delivered the message but instead continued marching in formation, then how far did he walk, given that he maintained a constant speed throughout his excursion?

I've tried calling the speed of the column v and the speed of the messenger u. I can say that

1/(u-v) + 1(u+v) = time taken

But I'm stuck as to what to do after this. Any help would be greatly appreciated!

 

[Londinium]

I'm not from the US so I don't know if this is the right category for it to be on, please do correct me.

 

[Dr.Peterson]

A column of soldiers a mile long is marching at constant speed. A messenger leaves his post at the rear of the column and walks to its front, where he delivers a message to his sergeant and then returns to his post. If he arrives back to exactly the position he would have found himself in had he not delivered the message but instead continued marching in formation, then how far did he walk, given that he maintained a constant speed throughout his excursion?

I've tried calling the speed of the column v and the speed of the messenger u. I can say that

1/(u-v) + 1(u+v) = time taken

But I'm stuck as to what to do after this. Any help would be greatly appreciated!

I think you meant "1/(u-v) + 1/(u+v) = time taken".

Just to clarify, you are measuring both speeds in miles per hour, and time in hours (or hours could be replaced by any other time unit), so that t = d/r and d = 1 mile. But I'm not sure why you used u-v and u+v; are you thinking in terms of relative speeds, or something else? I need to know how you are thinking in order to continue from where you left off.

But one thing you haven't done yet is to use the fact that "the time taken" is the same time it took the rear of the column to get to the same place. What is that?

I'm not from the US so I don't know if this is the right category for it to be on, please do correct me.

Your category is appropriate.