Reply To: Puzzles
Speed must go to the front of the column, so 10 miles, and then return to the rear, another 10 miles.
The time t1 of the outward journey is the distance divided by its speed. t1 = 10 / (v-1). (v-1 because the column is moving in the same direction).
The return time t2 is the distance divided by its speed. t2 = 10 / (v+1). (v+1 because the column is moving in the opposite direction).
t1 + t2 = 1 (one hour)
t1 + t2 = 10 / (v-1) + 10 / (v+1) = 1
[10(v+1) + 10(v-1)] / (v+1) * (v-1) = 1
(10v + 10 + 10 v -10) =( v² – 1)
20v = (v² – 1)
v² – 20v – 1 = 0
v = 10 + sqr(101) (the positive result)
Translated with DeepL.com (free version)