There is a 50m long army platoon marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position. In the mean time the whole platoon has moved ahead by 50m. The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.

2 Answers on this Question

1. The last person covered 120.71 meters.
   It is given that the platoon and the last person moved with
   uniform speed. Also, they both moved for the identical
   amount of time. Hence, the ratio of the distance they
   covered – while person moving forward and backword – are
   equal.
   Let’s assume that when the last person reached the first
   person, the platoon moved X meters forward.
   Thus, while moving forward the last person moved (50+X)
   meters whereas the platoon moved X meters.
   Similarly, while moving back the last person moved [50-(50-
   X)] X meters whereas the platoon moved (50-X) meters.
   Now, as the ratios are equal,
   (50+X)/X = X/(50-X)
   (50+X)*(50-X) = X*X
   Solving, X=35.355 meters
   Thus, total distance covered by the last person
   = (50+X) + X
   = 2*X + 50
   = 2*(35.355) + 50
   = 120.71 meters
   Note that at first glance, one might think that the total
   distance covered by the last person is 100 meters, as he
   ran the total lenght of the platoon (50 meters) twice.
   TRUE, but that’s the relative distance covered by the last
   person i.e. assuming that the platoon is stationary.

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2. 150 
   Since the platoon has covered 50m overall and they are moving with uniform speed, we can say it covers 25m when the man comes from last to first(forward) and another 25m when he comes last again(backward). 
   50m (platoon length)+25+50(platoon length)+25=150m

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