Question

Хозяин собаки шёл от дома со скоростью 80 м /мин.Через 5 мин за ним из дома выбежала собака и побежала со скоростью 280 м /мин.На каком расстоянии от дома собака догонит хозяина?

Answer 1

Пусть собака догонит на хозяина расстоянии х м от дома. Собака затратит на этот путь у минут, а хозяин у+5 минут.
Получаем систему:  
х/у=280;
х/(у+5)=80  

Выразим х их первого уравнения:
х=280у
И подставим во второе:  
280у/(у+5)=80
у/(у+5)=80/280
у/(у+5)=2/7  
7у=(у+5)*2
7у=2у+10
5у=10
у=2  

х=280*2=560  
Ответ: собака догонит хозяина на расстоянии 560 м от дома

Answer 2

Problem Analysis

We are given that the owner of a dog is walking away from their house at a speed of 80 m/min. After 5 minutes, the dog starts running from the house towards the owner at a speed of 280 m/min. We need to determine the distance from the house where the dog catches up to the owner.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the dog and the owner is the difference between their individual speeds. In this case, the relative speed is 280 m/min - 80 m/min = 200 m/min.

Since the dog starts running 5 minutes after the owner, we can calculate the distance the owner has covered in those 5 minutes. The distance covered by the owner in 5 minutes is given by the formula:

Distance = Speed × Time

Substituting the values, we have:

Distance = 80 m/min × 5 min = 400 m

Therefore, when the dog starts running, the owner is already 400 meters away from the house.

Now, we can calculate the time it takes for the dog to catch up to the owner. The time taken is given by the formula:

Time = Distance / Relative Speed

Substituting the values, we have:

Time = 400 m / 200 m/min = 2 min

Therefore, it will take the dog 2 minutes to catch up to the owner.

Finally, we can calculate the distance from the house where the dog catches up to the owner. The distance is given by the formula:

Distance = Speed × Time

Substituting the values, we have:

Distance = 280 m/min × 2 min = 560 m

Therefore, the dog will catch up to the owner at a distance of 560 meters from the house.

Answer

The dog will catch up to the owner at a distance of 560 meters from the house.