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Solution to: Spirited Soldier

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 travelled (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).

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