Question

Хозяин бежит со скоростью 80 м/мин а собака бежит за хозяином со скоростью 170 м/мин через сколько минут собака догонит хозяина если расстояние между ними 270м? 1) решите задачу с помощью схематического изображения. 2) решите задачу с составлением таблицы.

Answer 1

1) 170+80=250(м/мин)-скорость сближения
2) 270-250=20(мин)
Ответ: через 20 минут они встретятся.

Answer 2

Problem Statement

Хозяин бежит со скоростью 80 м/мин, а собака бежит за хозяином со скоростью 170 м/мин. Нам нужно определить, через сколько минут собака догонит хозяина, если расстояние между ними составляет 270 м.

Solution using a Schematic Diagram

To solve this problem using a schematic diagram, we can represent the distances covered by the owner and the dog over time. Let's assume that the time taken by the dog to catch up with the owner is 't' minutes.

At time t=0, the owner and the dog are at the same position. As time progresses, the owner covers a distance of 80t meters, while the dog covers a distance of 170t meters. Since the dog is running faster, it will catch up with the owner when the total distance covered by the dog is equal to the distance between them, which is 270 meters.

Using this information, we can set up the following equation: 80t + 270 = 170t

Simplifying the equation, we get: 90t = 270

Solving for t, we find: t = 3 minutes

Therefore, the dog will catch up with the owner in 3 minutes.

Solution using a Table

To solve this problem using a table, we can create a table to track the distances covered by the owner and the dog over time.

| Time (minutes) | Distance covered by the owner (meters) | Distance covered by the dog (meters) | |----------------|---------------------------------------|--------------------------------------| | 0 | 0 | 0 | | 1 | 80 | 170 | | 2 | 160 | 340 | | 3 | 240 | 510 | | 4 | 320 | 680 | | 5 | 400 | 850 |

From the table, we can see that at 3 minutes, the owner has covered a distance of 240 meters, while the dog has covered a distance of 510 meters. Since the dog has covered a greater distance, it will catch up with the owner at this time.

Therefore, the dog will catch up with the owner in 3 minutes.

Note: Both the schematic diagram and the table provide the same result, which is that the dog will catch up with the owner in 3 minutes.