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 backward - are equal.
Let's assume that when the last person reached the first person, the platoon moved X meters
Thus, while moving forward the last person moved (50+X) meters whereas the platoon moved X
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