Question

Два брата идут друг за другом со скоростями 2 м/с и 1.5 м/с. Один догоняет другого. Между ними, от одного к другому и обратно, бегает собачка, скорость которой 8 м/с. Определите путь (в метрах), который проделает собачка до встречи братьев. Начальное расстояние между братьями 150 м. Ответом является целое число, в случае необходимости округлите до целых.

Answer 1

Время сближения братьев t = L/(v1 + v2) (1), где (v1 + v2) – их скорость относительно друг друга. Путь, проделанный собачкой за это время, s = v3t = Lv3/(v1 + v2) (2); s = 160 м.

Answer 2

Problem Analysis

We are given that two brothers are walking one after the other with speeds of 2 m/s and 1.5 m/s. There is a dog running between them and back at a speed of 8 m/s. We need to determine the distance the dog travels before meeting the brothers. The initial distance between the brothers is 150 m.

Solution

To solve this problem, we need to find the time it takes for the faster brother to catch up to the slower brother. Once we have the time, we can calculate the distance the dog travels by multiplying its speed by the time.

Let's denote the distance traveled by the faster brother as x. The time it takes for the faster brother to catch up to the slower brother is given by:

Time = Distance / Relative Speed

The relative speed between the brothers is the difference in their speeds:

Relative Speed = Speed of Faster Brother - Speed of Slower Brother

Substituting the given values, we have:

Relative Speed = 2 m/s - 1.5 m/s = 0.5 m/s

Now, we can calculate the time it takes for the faster brother to catch up to the slower brother:

Time = 150 m / 0.5 m/s = 300 seconds

Finally, we can calculate the distance the dog travels by multiplying its speed by the time:

Distance = Speed of Dog * Time = 8 m/s * 300 seconds = 2400 meters

Therefore, the dog travels a distance of 2400 meters before meeting the brothers.

Answer

The dog travels a distance of 2400 meters before meeting the brothers.