Question

Колонна туристов длиной L=75 метров движется с постоянной скоростью. Курьер, движущийся в 2 раза быстрее колонны, бежит с поручением от хвоста к голове колонны и обратно. Найдите путь, который пробежал курьер, выполняя поручение.

Answer 1

Обозначим:
Скорость колонны туристов V
Скорость курьера 2V

Далее надо перейти в систему отсчета, связанную с колонной туристов. В этой системе отсчета колонна стоит на месте, а скорость курьера будет:
 
Vотн1= 2V-V=V

при движении к голове колонны и

Vотн2= 2V+V=3V

при движении от головы колонны к хвосту.

Таким образом, исходная задача сводится к следующей задаче: За какое время (Т) курьер двигаясь со скоростью Vотн1 пройдет от хвоста неподвижной колонны длиной 75 метров до ее начала и обратно, если на обратном пути его скорость будет Vотн2. Получаем:

Т= 75/Vотн1+ 75/Vотн2 = 75/V+75/3V = 100/V

В системе координат, связанных с дорогой (относительно которой колонна движется со скоростью V, а курьер 2V) курьер пройдет за то же время (Т) путь (S)

S=Т*2V= ((100)/V)*2V=200 метров

Ответ: 200 метров

Answer 2

Problem Analysis

We are given a column of tourists with a length of L = 75 meters, moving at a constant speed. A courier, who moves twice as fast as the column, runs from the tail to the head of the column and back. We need to find the distance covered by the courier while performing this task.

Solution

To find the distance covered by the courier, we need to calculate the total distance covered while running from the tail to the head of the column and back.

Let's assume the speed of the column is v meters per second. Since the courier moves twice as fast as the column, the speed of the courier is 2v meters per second.

The time taken by the courier to run from the tail to the head of the column is equal to the length of the column divided by the speed of the courier. Similarly, the time taken by the courier to run from the head to the tail of the column is also equal to the length of the column divided by the speed of the courier.

Therefore, the total distance covered by the courier is equal to the sum of the distances covered while running from the tail to the head and from the head to the tail of the column.

Let's calculate the distance covered by the courier.

Calculation

Given: Length of the column, L = 75 meters Speed of the column, v = unknown Speed of the courier, 2v = unknown

To find the distance covered by the courier, we need to calculate the total distance covered while running from the tail to the head of the column and back.

The time taken by the courier to run from the tail to the head of the column is equal to the length of the column divided by the speed of the courier. Similarly, the time taken by the courier to run from the head to the tail of the column is also equal to the length of the column divided by the speed of the courier.

Therefore, the total distance covered by the courier is equal to the sum of the distances covered while running from the tail to the head and from the head to the tail of the column.

Let's calculate the distance covered by the courier.

Distance covered from the tail to the head of the column: Distance = Speed * Time Distance = 2v * (L / (2v)) Distance = L

Distance covered from the head to the tail of the column: Distance = Speed * Time Distance = 2v * (L / (2v)) Distance = L

Total distance covered by the courier: Total Distance = Distance from tail to head + Distance from head to tail Total Distance = L + L Total Distance = 2L Total Distance = 2 * 75 Total Distance = 150 meters

Therefore, the courier covers a distance of 150 meters while performing the task.

Answer

The courier covers a distance of 150 meters while performing the task.

Note: The sources provided did not contain the specific information required to answer this question. Therefore, the answer is based on mathematical reasoning and does not require external sources.