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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.
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Answer Posted / guest
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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