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

Question

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.

Answer 1

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).

Answer 2

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