SOLUTION: an army of soldiers is marching down a road at 5 mph. a messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. assu
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Question 96220: an army of soldiers is marching down a road at 5 mph. a messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. assuming that the messenger rides at the rate of 10 mph, determine the distance from the front to the rear.
Found 3 solutions by ankor@dixie-net.com, aajayunlimited, ikleyn:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An army of soldiers is marching down a road at 5 mph. a messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. assuming that the messenger rides at the rate of 10 mph, determine the distance from the front to the rear.
:
To convert mph to ft/min: 5280/60 = 88
:
Speed in ft/min, relative to the troops:
Riding against the troop direction: 88(10+5) = 1320 ft/min
Riding with the troop direction: 88(10-5) = 440 ft/min
:
Let x = length of the troops, from front to rear, in ft:
Write a time equation (in min): Time = distance/speed (in ft/min)
+ = 10
:
Get rid of the denominators, mult equation by 1320
x + 3x = 1320(10)
4x = 13200
x = 13200/4
x = 3300 ft is the length of the troop
:
In miles: 3300/5280 = 5/8 of a mile
:
:
Check our solution, find the time for the trip back, and return trip
3300/1320 = 2.5 min to the rear
3300/440 = 7.5 min return
----------------------------
total time = 10 min
Answer by aajayunlimited(1) (Show Source): You can put this solution on YOUR website!
I noticed that you could eliminate the ft/min step. ankor was right, but it gets even simpler. Formula needed: t = d / r. | Then, d / r[a] + d / r[b] = t. | Fill in for "r" and "t". | d/10 - 5 + d/10 + 5 = 10 minutes. | Convert 10 minutes to 1/6 hrs. | Next, d/5 + d/15 = 1/6. | Multiply each part by 30 to get rid of fractions. | Now, the equation becomes 6d + 2d = 5 | Last, solve: d = 5/8 of a mi. JUST ADDING TO ANKOR(A SIMPLIER METHOD)--THIS PROBLEM WAS ALREADY SOLVED IN A SIMILIAR FASHION BY ANKOR@DIXIE.NET.
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
Let be the length of army's column (line) in miles.
When the messenger is moving from the front to the rear, he moves in the direction opposite the the army's move. Therefore, his speed relative to the army's column is = , and he spends hours to get from the front to the rear.
On the way back the messenger moves in the same direction as the army's column moves. Therefore, his speed relative to the army's column is = , and he spends hours to get from the rear to the front.
Therefore, the equation is
+ = (10 minutes = of hour).
Solve it by simplifying step by step:
+ = ,
d + 3d = ,
4d = ,
d = miles.
Answer. The distance from the front to the rear is miles.
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