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29. Marching Army

An army column is four miles long and is marching at four miles per hour. A horse rider sets off from the back of the column and rides at a speed of eight miles per hour to deliver a message to the general at the front of the column. He delivers the message, turns straight round and rides back to the end of the column.

How far does the rider travel?

Scroll down the page for the answer.

The rider's journey is in two parts:

1. Riding to the front of the column, the rider's speed relative to the army is (8 - 4 =) 4 mph and since the column is 4 miles long, the rider takes 1 hour to reach the front.

So if (s)he has been riding for 1 hour then the actual distance covered is 8 miles.

2. On the return journey the rider's speed, relative to the column, is (8 + 4 =) 12 mph so the time taken to travel the equivalent of four miles to the back of the column is 4/12 = 1/3 hour.

In 1/3 hour the actual distance covered by the rider is 8/3 miles

The total distance travelled, then, is

8 + 8/3 = 10 2/3 miles

This is, perhaps, not an intuitive answer but we leave it to you to generalise the solution for variable length columns and different speeds of army and rider. Discuss!!

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