Question

4. Вдоль железной дороги через каждые 100 м расставлены столбики с номерами 1, 2, . . . , 10, 1, 2, . . . , 10, . . . . Через 2 минуты после того, как кабина машиниста равномерно движущегося поезда проехала столбик с номером «1», машинист увидел в окне столбик с номером «2». Через какое наименьшее время (в с) после проезда этого столбика кабина машиниста может проехать мимо ближайшего столбика с номером «3»? Скорость поезда меньше 100 км/ч. Ответ укажите с точностью до десятых.

Answer 1

Problem Analysis

We are given that along a railway track, there are poles with numbers from 1 to 10, and then the sequence repeats. The train passes pole 1, and after 2 minutes, the train passes pole 2. We need to determine the minimum time it will take for the train to pass the next pole with the number 3.

Solution

To solve this problem, we need to determine the time it takes for the train to travel the distance between two consecutive poles. Since the distance between each pole is 100 meters, we can calculate the speed of the train using the formula:

Speed = Distance / Time

Let's assume that the speed of the train is v meters per minute. We can calculate the time it takes for the train to travel 100 meters using the formula:

Time = Distance / Speed = 100 / v

Since the train passes pole 1 and then pole 2 in 2 minutes, we can set up the following equation:

2 = Time to pass pole 1 + Time to pass pole 2 = 100 / v + 100 / v

Simplifying the equation, we get:

2 = 200 / v

Solving for v, we find:

v = 200 / 2 = 100 meters per minute

Now that we know the speed of the train, we can calculate the time it takes for the train to pass pole 3:

Time to pass pole 3 = Distance / Speed = 100 / 100 = 1 minute

Therefore, the train will pass the next pole with the number 3 in 1 minute.

Answer

The train will pass the next pole with the number 3 in 1 minute.