An army 50 miles long marches at a constant rate. A courier standing at the rear movesforward and delivers the message to the first person and then turns back and reaches therear of the army as the army completes 50 miles. Find the distance travelled by the courier

Madhusmita_behera
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Sep 21st, 2006
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guhakoushik
Profile Answers by guhakoushik

Dec 21st, 2010

Suppose, speed of army = v miles/hr.
speed of courier = w miles/hr.
Suppose the courier reached the first person at 50 + x miles from the starting.
Let the time taken by both to reach 50+x distance is t hr. and time taken by both to reach 100 miles is s hr.

Now we get,

                x = v * t;
                50 + x = w * t;

                50 = v * s;
                2x + 50 = w * s;

By solving these equations we get,
                x=35;

So the distance traveled by courier = 2 * 35 + 50
                                                  = 120 miles.