Question

Помогите решить задачу. Срочно!! Скорость двух пешеходов 4 км/ч и 6 км/ч. Они вышли навстречу друг другу из Минска и Самохвалович из точек, расстояние между которыми 20 км. Одновременно с первым навстречу второму выбежала собака со скоростью 20 км/ч. Добежав до второго пешехода она развернулась и побежала обратно до встречи с первым. При встрече с первым снова развернулась и побежала навстречу второму и так далее, пока пешеходы не встретились. Какое расстояние пробежала собака?

Answer 1

20 км раздели на 4км/ч и потом умнож на 20 будет 100км

Answer 2

Problem Analysis

To solve this problem, we need to determine the distance the dog ran before the two pedestrians met. We are given the speeds of the pedestrians and the distance between them, as well as the speed of the dog. The dog runs towards one pedestrian, then turns around and runs back towards the other pedestrian, repeating this pattern until the pedestrians meet.

Solution

Let's break down the problem step by step:

1. Calculate the time it takes for the pedestrians to meet: - The combined speed of the pedestrians is 4 km/h + 6 km/h = 10 km/h. - The distance between the pedestrians is 20 km. - Using the formula `time = distance / speed`, the time it takes for the pedestrians to meet is 20 km / 10 km/h = 2 hours.

2. Calculate the distance the dog runs in one round trip: - The dog's speed is 20 km/h. - The time it takes for the pedestrians to meet is 2 hours. - The distance the dog runs in one round trip is the product of its speed and the time it takes for the pedestrians to meet: 20 km/h * 2 hours = 40 km.

3. Calculate the number of round trips the dog makes before the pedestrians meet: - The distance between the pedestrians is 20 km. - The distance the dog runs in one round trip is 40 km. - The number of round trips the dog makes is the distance between the pedestrians divided by the distance the dog runs in one round trip: 20 km / 40 km = 0.5 round trips.

4. Calculate the distance the dog runs before the pedestrians meet: - The distance the dog runs in one round trip is 40 km. - The number of round trips the dog makes is 0.5 round trips. - The distance the dog runs before the pedestrians meet is the product of the distance the dog runs in one round trip and the number of round trips: 40 km * 0.5 round trips = 20 km.

Therefore, the dog runs a distance of 20 km before the pedestrians meet.

Answer

The dog runs a distance of 20 km before the pedestrians meet.