From the middle of the convoy, moving at a speed of 10 km / h, two motorcyclists are leaving at the same time

From the middle of the convoy, moving at a speed of 10 km / h, two motorcyclists are leaving at the same time, one at the head of the column and the other at the tail. How fast did the motorcyclists move if their speeds were the same, and the travel time of one motorcyclist was half that of the other?

Let the speeds of two motorcyclists leaving the middle of a convoy of cars with a length of 2 ∙ S at the same time be the same: v₁ = v₂ = v, and the speed of the column v₀ = 10 km / h, then:

(v + 10) km / h – the speed of the motorcyclist relative to the column, moving towards the head of the column;

(v – 10) km / h – the speed of the motorcyclist relative to the column, moving towards the tail of the column;

S / (v + 10) h – time of movement of the motorcyclist relative to the column, moving towards the head of the column;

S / (v – 10) h – time of movement of the motorcyclist relative to the column, moving towards the tail of the column.

Knowing that the time of movement of one motorcyclist turned out to be half that of another, the time of movement of another, we obtain the equation: 2 · S / (v + 10) = S / (v – 10); x = 30 (km / h) – motorcyclists’ own speed.

Answer: motorcyclists were moving at a speed of 30 km / h.