Solution for calculating the distance

Question:  http://good-interview-puzzles.blogspot.com/2011/09/calculate-distance.html

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 distancethey covered - while person moving forward and backword - are equal.Let's assume that when the last person reached the first person, the platoonmoved X meters forward.Thus, while moving forward the last person moved (50+X) meters whereas theplatoon moved X meters
Similarly, while moving back the last person moved [50-(50-X)] X meterswhereas the platoon moved (50-X) meters.
 Now, as the ratios are equal,(50+X)/X = X/(50-X)(50+X)*(50-X) = X*XSolving, X=35.355 metersThus, total distance covered by the last person= (50+X) + X= 2*X + 50= 2*(35.355) + 50= 120.71 metersNote that at first glance, one might think that the total distance covered by thelast 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 

calculate the distance

There is a 50m long army platoon marching ahead. The last person in the platoonwants to give a letter to the first person leading the platoon. So while the platoon ismarching he runs ahead, reaches the first person and hands over the letter to him andwithout 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.

Solution is   http://good-interview-puzzles.blogspot.com/2011/09/solution-for-calculating-distance-it-is.html