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A troop 5 metres long starts marching. A soldier at the end of the file steps out and starts marching at a higher speed. On reaching the head of the column , he immediately turns around and marches back at the same speed. As soon as he reaches the end of the file, the troop stops marching and is found to have travelled 5 metres exactly. What distance has the soldier travelled?

veronica
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  • Was he soldier Mahalanobis or soldier Euclid ? –  May 03 '16 at 16:13
  • look i had to enter a field........so i entered it at random! sorry for that.......... why do u care whosoever it was ........if u didn't care to answer my question !! :P @Yves Daoust – veronica May 03 '16 at 17:29
  • almagest's answer was good enough. But ill-tagged questions are polluting the site. The Mahalanobis distance is used in stats only. –  May 03 '16 at 17:49
  • i already apologised...........i just couldn't think of one! @Yves Daoust – veronica May 03 '16 at 18:01

1 Answers1

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Suppose the troop marches a distance $d$ before the soldier turns around. Then the soldier has marched a distance $5+d$, so he is marching $\frac{5+d}{d}$ times faster. Having turned around the troop marches a distance $5-d$ before he gets back to his position and he marches a distance $d$. So $\frac{d}{5-d}=\frac{5+d}{d}$. Hence $d=\frac{5}{\sqrt2}$. The soldier marches a total distance $5+2d=5(1+\sqrt2)$.

almagest
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