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## Question

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.

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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 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.

let x be the distance covered by the first person in the platoon until the time the letter is given to him.

The last person (the one with the letter) needs to cover 50+x while the first needs to cover x.

Over the total time it takes to get back into position, the last person covers 2x+50 while the first covers 50.

The ratios of these need to be equal since their speeds are constant.

Cross multiplying results in 2x^2+50x = 50x + 2500.

2x^2 = 2500

x^2 = 1250

x = 25 * sqrt(2)

So the total distance the soldier covers is 2x+50 = 50 * sqrt(2) + 50.

This is approximately 120.71m

Edited by EventHorizon

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

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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.

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

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.

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you are both wrong. first, he has to travel more than 50m forward to get to the leader. then he will travel less than 50m to get to the rear.

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.

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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.

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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.

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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 ...

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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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i agree with eventhorizon completely.

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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.

ya, I agree. My point was to stress the original and new locations are different. Thanx for the correction.

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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.

Wait, is the answer a number? I thought it had to include some sort of variable -- I think the answer is

(100a^2)/(a^2 - b^2) where a is speed of soldier and b is the speed of the platoon

thank you

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Say the runner moves faster than the platoon by a factor a.

When he reaches the front, the platoon has moved a distance x.

That means a = [x + 50]/x = 1 + 50/x.

When he returns to the rear, the platoon has moved 50m and the runner 50 + 2x.

That means a = [50 + 2x]/50 = 1 + x/25.

Thus 50/x = x/25 or x = 25 sqrt(2).

The runner thus ran 50[1+sqrt(2)] = 120.71 meters

Kudos to EventHorizon for getting it first.

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Say the runner moves faster than the platoon by a factor a.

When he reaches the front, the platoon has moved a distance x.

That means a = [x + 50]/x = 1 + 50/x.

When he returns to the rear, the platoon has moved 50m and the runner 50 + 2x.

That means a = [50 + 2x]/50 = 1 + x/25.

Thus 50/x = x/25 or x = 25 sqrt(2).

The runner thus ran 50[1+sqrt(2)] = 120.71 meters

sorry i found dumb, but how do we know the platoon went 50m when the soldier went back?

i thought that say the platoon barely moves and the soldier rans ultra fast (instanteous)

then the soldier ran 100 m

how are we coming out with a specific number? like 120.71 m?

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sorry i found dumb, but how do we know the platoon went 50m when the soldier went back?

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LOL - paint me embarassed

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I get how yall did the whole math part, but what if the total distance is looked at as positive for forward and negitive for the return

then the total distance traveled by the soldier would be the same as the rest of the platoon

50 m

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Wait, is the answer a number? I thought it had to include some sort of variable -- I think the answer is

Strykr,

ya, the answer is a real number.

sorry i found dumb, but how do we know the platoon went 50m when the soldier went back?

In my original post, I said while the soldier was delivering the letter, the whole platoon moved ahead by 50m.

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?

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I get how yall did the whole math part, but what if the total distance is looked at as positive for forward and negitive for the return

then the total distance traveled by the soldier would be the same as the rest of the platoon

50 m

Thatguyagain,

In that case, I would have used 'displacement' rather than distance. Don't you think so?

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i may be wrong but i think it's just 50m. If not then it's 50 plus an unspecified number.

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