A column of tourists with a length of L = 75 meters is moving at a constant speed. A courier moving 2 times faster

A column of tourists with a length of L = 75 meters is moving at a constant speed. A courier moving 2 times faster than the column runs from the tail to the head of the column and back. Find the path that the courier ran while completing the assignment.

Given:

L = 75 meters – the length of the column with tourists;

v1 = v – speed of the column with tourists;

v2 = 2 * v – courier movement speed.

It is required to find S (meters) – the path that the courier traveled, passing orders from the beginning of the column to the end and back.

The courier’s speed in the coordinate system associated with the column will be:

v00 = v1 + v2 = v + 2 * v = 3 * v – when the courier moves to the end of the column;

v01 = v2 – v1 = v – when the courier moves to the beginning of the column.

Then, the total time of the courier’s movement will be equal to:

t = L / 3 * v + L / v = L + 3 * L / 3 * v = 4 * L / (3 * v).

In the coordinate system associated with the road, during this time the courier will cover the path:

S = 2 * v * t = 2 * v * 4 * L / (3 * v) = 8 * L / 3 = 8 * 75/3 = 200 meters.

Answer: the courier will travel a distance of 200 meters.