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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.
**Skip to the answer!**

** What was the puzzle?**
Let's suppose the first person of the platoon move **X meters** ahead by the time the last person reaches to him.

To reach at him, the last person has to cover distance of **50 + x.**

Assume **M** be the **speed of last person** and **P** be the **speed of platoon** i.e. of first person.

If **T1** is time needed for the last person to get to at the first person,

T1 = (50 + X)/M

T1 = X/P

(50 + X)/M = X/P

**M/P = (50 + X)/X ..........(1)**

As per given data, by the time the last person gets back to it's original position (i.e. end of platoon), the platoon moves **50m ahead** from it's position that was when the last person started his journey towards first person.
That is end of platoon is now at position at which the start of platoon was initially.

Since, the first person has already moved **X meters** ahead, he has to move only **50 - X** meter to lead the platoon 50m ahead of it's original position.

And, the last person has to move only **X meters** to get back to original position i.e. the end of platoon.

If **T2** is the time taken by last person to get back to original position (i.e. time taken by first person to move ahead 50 - x) then,

T2 = X/M

T2 = (50 - X)/P

X/M = (50 - X)/P

**M/P = X/(50 - X) ..........(2)**

Equating (1) and (2),

(50 + X)/X = X/(50 - X)

X^2 = (50 + X)(50 - X)

X^2 = 2500 - X^2

X^2 = 1250

**X = 35.355 meters.**

So,

the distance traveled by the last person = (50 + X) + X
= (50 +35.355) + 35.355
the distance traveled by the last person = **120.71 meters.**

The ratio of their speeds = M/P = (50 + X)/X = (50 + 35.355)/35.355 = 2.41

M = 2.41 P

That is the speed of last man is 2.41 times the speed of first man or the speed of platoon itself.

And that's the speed the last man needed to reach at the first person of the platoon.