Question 980173


Let  {{{d}}}  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  {{{10+5}}} = {{{15}}} {{{mi/h}}},  and he spends  {{{d/15}}}  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  {{{10-5}}} = {{{5}}} {{{mi/h}}},  and he spends  {{{d/5}}} hours to get from the rear to the front.


Therefore,  the equation is


{{{d/15}}} + {{{d/5}}} = {{{1/6}}}      (10 minutes = {{{1/6}}} of hour).


Solve it by simplifying step by step:


{{{d/15}}} + {{{3d/15}}} = {{{1/6}}},


d + 3d = {{{15/6}}},


4d = {{{15/6}}},


d = {{{15/24}}} miles.


<B>Answer</B>.  &nbsp;The distance from the front to the rear is &nbsp;{{{15/24}}}&nbsp; miles.