## 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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