As soon as an army 1 mile long begins to march, a courier leaves the rear of the army for the front. The courier reaches the front and immediately turns back for the rear; the courier reaches the rear after the army has traveled 1 mile. How far did the courier travel?
2007-11-10 15:35:15 · 20 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Let's suppose that the army had marched D miles by the time he catches up with them. Then he had to run (1+D) miles in the same amount of time that they went D miles.
He doubles back and runs another D miles to get back to the one mile mark. So, he runs 1+2D in the time it takes the army to walk a full mile.
If we assume that everyone moves at the same pace at all times, we get the ratio of (1+D)/D = (1+2D)/1
this means that:
(1+D) = (D+2D^2)
This means that 2D^2-1 = 0
So -- D = SQRT(1/2).
This means that he ran a total of 1+2*sqrt(1/2) miles which is around 2.414 miles.
2007-11-10 16:23:28 · answer #1 · answered by Ranto 7 · 2⤊ 0⤋
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2016-09-29 00:07:52 · answer #2 · answered by coughlan 4 · 0⤊ 0⤋
The courier has to travel over a mile to get to the front then travel less than a mile back. I say he has to travel a total of 2 miles
2007-11-10 15:42:37 · answer #3 · answered by Tommiecat 7 · 0⤊ 2⤋
one mile, because he went up to the front which is a mile and she just turned around and the army marched the other mile so he only actually traveled a mile.
2007-11-10 15:38:40 · answer #4 · answered by adsklfjadlgj 2 · 1⤊ 2⤋
2 miles
2007-11-10 15:44:47 · answer #5 · answered by Anonymous · 0⤊ 2⤋
2 miles
2007-11-10 15:39:55 · answer #6 · answered by Anonymous · 0⤊ 3⤋
he may have walked 2 miles, however from point A to point B he only traveled 1 mile
2007-11-10 15:44:30 · answer #7 · answered by lisa n 3 · 1⤊ 2⤋
2 miles because he traveled the length of the army twice
2007-11-10 15:39:31 · answer #8 · answered by Photo Girl 3 · 0⤊ 3⤋
3 miles.
2007-11-10 15:38:57 · answer #9 · answered by !~"Fish On"~! 5 · 0⤊ 3⤋
two miles.
The speed of the march is added to the forward leg, but subtracted from the reverse direction leg. Since its given as a constant, it's self-negating, leaving only the travel distance to and from the opposing ends of the column.
2007-11-10 15:50:46 · answer #10 · answered by omnisource 6 · 1⤊ 2⤋