Distance covered - One puzzle a day - Puzzle Buddies

Puzzle:There is a 50 m long army platoon marching ahead. The last person in the platoon wants to give a letter to 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 by 50 m.

The question is how much distance did the last person cover in that time assuming that he ran the whole distance with uniform speed.
Note: Don't forget to visit us again. Answer to the puzzle will be posted tomorrow with winner's name. You can provide your answer in comments.
Solution: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  

Winner: