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### #1

Posted 04 March 2008 - 07:41 PM

You may assume that he ran the whole distance with uniform speed, and of course the platoon were marching at a uniform speed.

### #2

Posted 04 March 2008 - 09:05 PM

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 during that time?

You may assume that he ran the whole distance with uniform speed, and of course the platoon were marching at a uniform speed.

**Edited by EventHorizon, 04 March 2008 - 09:06 PM.**

### #3

Posted 04 March 2008 - 09:05 PM

### #4

Posted 04 March 2008 - 09:08 PM

100m. 50m to deliver the mail to the front then 50m to run back.

That would be true if the platoon wasn't moving. The platoon moves forward 50m during this whole process.

### #5

Posted 04 March 2008 - 10:04 PM

It would still be 100m. 50 + x (where x is the distance the platoon moved while he was running to the front) and 50 - x as he returned to the back of the platoon. As long as his speed is constant both ways and the platoon speed is constant he will save as much distance returning as he had to go extra to get to the front.That would be true if the platoon wasn't moving. The platoon moves forward 50m during this whole process.

### #6

Posted 04 March 2008 - 10:10 PM

second, i can understand how you are getting 2x + 50 since x has to be 2 different numbers (1 before letter, 2 after getting letter). I could be mistaken but i don't have a solution i can live with yet.

### #7

Posted 04 March 2008 - 10:14 PM

It would still be 100m. 50 + x (where x is the distance the platoon moved while he was running to the front) and 50 - x as he returned to the back of the platoon. As long as his speed is constant both ways and the platoon speed is constant he will save as much distance returning as he had to go extra to get to the front.

To get to where he will need to eventually be, he would need to move 50m.

From there, he needs to move x more to reach the leader.

He then needs to move x back....not 50-x.... to get back into position.

### #8

Posted 04 March 2008 - 10:17 PM

It would still be 100m. 50 + x (where x is the distance the platoon moved while he was running to the front) and 50 - x as he returned to the back of the platoon. As long as his speed is constant both ways and the platoon speed is constant he will save as much distance returning as he had to go extra to get to the front.

DrHim,

That would make the soldier to return to his original position. But the soldier's new location is different (actually 50m away) from his original one.

### #9

Posted 04 March 2008 - 10:19 PM

To get to where he will need to eventually be, he would need to move 50m.

From there, he needs to move x more to reach the leader.

He then needs to move x back....not 50-x.... to get back into position.

Exactly ...

### #10

Posted 04 March 2008 - 10:23 PM

DrHim,

That would make the soldier to return to his original position. But the soldier's new location is different (actually 50m away) from his original one.

He would need to go 50 + x backwards to reach his original position.

50-x would be the distance the soldier would need to go _forward_ after delivering the letter to be where the leading soldier will be once the platoon moved 50m.

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