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 × √2 km/h (approximately 14.49 km/h).
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