# Thread: How long did the messenger march?

1. ## How long did the messenger march?

A column of soldiers is 25 miles long and they march 25 miles a day One morning a messenger started at the rear of the column with a message for the guy up front. The messenger began to march and gave the message to the guy up front and then returned to his position by the end of the day. Assume that the messenger marched at the same rate of speed the whole time. How many miles did the messenger march?

2. ## Re: How long did the messenger march?

I think the answer is 25 (1+ sqrt(2)). Am i correct?

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suresh

3. ## Re: How long did the messenger march?

Yes. But you need to give us your solution here

4. ## Re: How long did the messenger march?

i think he marched 25 miles

5. ## Re: How long did the messenger march?

Please give the solution. I couldn't understand how the answer is got.

6. ## Re: How long did the messenger march?

The answer is (25 + (50/sqrt(2))) miles.

Here is the solution:
Assume by the time the messenger met him, the guy upfront had marched x miles. When the met the messenger might have marched (25+x) miles and the guy upfront might have marched x miles.

After they met, till the end of the day, the guy upfront might have marched (25-x) miles and the messenger might have marched back x miles to take his position (by the end of the day, the last guy in the column might have marched 25 miles).

Putting them in equation yields: (25 + x)/x = x/(25 - x)

From it we get: x = 25/sqrt(2).

The messenger might have marched a complete distance of 25 + 2*x miles in the whole day yielding: (25 + (50/sqrt(2))) miles.

7. ## Re: How long did the messenger march?

its 75 miles

8.

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