Question

Из пункта A в пункт B вышел пешеход. Одновременно с ним из B в A выехал велосипедист. Через 2 часа пешеход находился от велосипедиста в 5 раз дальше, чем от пункта A. Еще через два часа произошла их встреча, после которой оба продолжили путь. Сколько часов занял путь велосипедиста от B до A?

Answer 1

Ответ:

12

Пошаговое объяснение:

13-1

Answer 2

Problem Analysis

We are given that a pedestrian and a cyclist start their journey simultaneously from points A and B, respectively. After 2 hours, the pedestrian is 5 times further from the cyclist than from point A. Two hours later, they meet and continue their journey. We need to determine how long the cyclist's journey took from point B to point A.

Solution

Let's assume that the distance between points A and B is d.

After 2 hours, the pedestrian is 5 times further from the cyclist than from point A. This means that the pedestrian has covered 5d in 2 hours, while the cyclist has covered d - 5d = -4d in the same time. The negative sign indicates that the cyclist is moving in the opposite direction.

Two hours later, they meet. At this point, the pedestrian has covered a total distance of 5d + 2(5d) = 15d, while the cyclist has covered a total distance of -4d + 2(-4d) = -12d.

Since they meet, the total distance covered by both the pedestrian and the cyclist must be equal. Therefore, we can set up the following equation:

15d = -12d

Simplifying the equation, we get:

27d = 0

Dividing both sides by 27, we find that d = 0.

This means that the distance between points A and B is 0, indicating that they are the same point.

Since the distance between points A and B is 0, the cyclist's journey from point B to point A also takes 0 hours.

Answer

The cyclist's journey from point B to point A takes 0 hours.

Explanation

The given problem states that the pedestrian and the cyclist start their journey simultaneously from points A and B, respectively. After 2 hours, the pedestrian is 5 times further from the cyclist than from point A. Two hours later, they meet and continue their journey. We need to determine how long the cyclist's journey took from point B to point A.

To solve this problem, we can assume that the distance between points A and B is d. After 2 hours, the pedestrian has covered 5d and the cyclist has covered -4d. Two hours later, they meet, and the total distance covered by both the pedestrian and the cyclist must be equal. Setting up the equation 15d = -12d, we find that d = 0. This means that points A and B are the same point, and the cyclist's journey from point B to point A takes 0 hours.

Please let me know if anything is unclear or if you have any further questions!