# How fast did the courier bike, when he delivers a letter on moving column?

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A military column of 1 km length marches with a constant speed of 6 kilometers per hour. A courier from the back of the column is sent to the head of the column by bike to deliver a message. Arrived at the front, he instantly returns. When he returns at the back, the column has traveled a distance of 1 km since the start of his errand. The courier drove with constant speed.

posted Feb 12, 2014

## 2 Solutions

+1 vote

The relative speed of the courier (compared to the column) is v-6 on the journey to the front, and v+6 on the way back. The distance traveled (relatively to the column) by the courier is in both cases 1 km, therefore the total time he is biking is

``````1       +      1
v - 6        v + 6
``````

The column travels 1 km in 10 minutes (1/6 hour), therefore

``````   1    +      1    = 1/6
v - 6      v + 6
``````

This can be written as a quadratic equation (v+6) + (v-6) = (v-6) × (v+6) / 6 with as only allowed solution v = 6 + 6 × sqrt(2) km/h (approximately 14.49 km/h).

solution Feb 12, 2014

Dear ans is 12 km/hr.............too easy

solution Oct 20, 2015

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