SOLUTION: A one kilometer long caravan of men is walking at a constant rate. A man from the rear end walks towards the head and back to the rear at the instant when the caravan has covered a

Question 1079571: A one kilometer long caravan of men is walking at a constant rate. A man from the rear end walks towards the head and back to the rear at the instant when the caravan has covered a distance of one kilometer. Find the total distance travelled by the man.
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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A one kilometer long caravan of men is walking at a constant rate. A man from the rear end walks towards the head and back
to the rear at the instant when the caravan has covered a distance of one kilometer. Find the total distance travelled by the man.
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Similar problem was submitted to the forum long time ago.
I solved it and posted as my answer to the forum; after that I placed it as the part of the lesson
    - Travel problems on a messenger moving back and forth along the marching army's column
in this site.


Surely, another numerical data were used in that problem, but it doesn't matter.
The answer is: 

  
     The distance traveled by the man is doubled length of the caravan, i.e. 2 km.


My solution was based on using the traditional coordinate system attached to the Earth surface.


Some time after that another tutor delivered another solution using coordinate system attached to the moving caravan.
In this coordinate system the caravan is UNMOVED, and the answer becomes crystally clear: 

          The distance traveled by the man is 2 times the length of the caravan.


It is true for ANY length of the caravan and for any speed of the man provided it is greater than the caravan's speed.

If you love Travel and Distance problems (as much as I love them), you can find A LOT of THEM in this site.

They are collected in the chapter Travel and Distance problems in this free of charge online textbook
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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