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 traveled (relative to the column) by the courier is 1 kilometer in both cases. Therefore, the total time he spends biking is:

The column travels 1 kilometer in 10 minutes (or ¹⁄₆ hour). Therefore, we have:

This can be rewritten as a quadratic equation: (v + 6) + (v - 6) = (v - 6) × (v + 6) / 6. The only valid solution is v = 6 + 6 × √2 km/h (approximately 14.49 km/h).

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