Question

Три машинки Двигаются по замкнутой трассе общей длиной 96 м. Скорость первой — 12 м/с, второй - 24 м/с, а третьей — среднее арифметическое между скоростями первой и второй. Каким должен быть самый большой промежуток времени между стартом двух из этих трёх машинок из одной ТОЧКИ, если все три машИНКИ После прохождения трассы вернулись к этой же точке к одному и тому же времени

Answer 1

скорей всего 1 и 3 Я так думаю

Answer 2

Problem Analysis

We are given three cars moving on a closed track with a total length of 96 m. The speed of the first car is 12 m/s, the speed of the second car is 24 m/s, and the speed of the third car is the arithmetic mean (average) of the speeds of the first and second cars. We need to determine the maximum time interval between the start of any two of these three cars from the same point, assuming they all return to the same point at the same time.

Solution

To find the maximum time interval between the start of any two cars, we need to consider the scenario where the cars are as far apart as possible when they start. This means that the first car should be at the starting point, the second car should be at the midpoint of the track, and the third car should be at the farthest point from the starting point.

Let's calculate the distances traveled by each car to reach these positions.

The total length of the track is 96 m. Therefore, the midpoint of the track is at a distance of 48 m from the starting point.

The first car travels at a speed of 12 m/s. To reach the starting point, it takes: Time taken by the first car to reach the starting point = Distance / Speed = 0 m / 12 m/s = 0 s

The second car travels at a speed of 24 m/s. To reach the midpoint of the track, it takes: Time taken by the second car to reach the midpoint = Distance / Speed = 48 m / 24 m/s = 2 s

The third car travels at the average speed of the first and second cars, which is (12 m/s + 24 m/s) / 2 = 18 m/s. To reach the farthest point from the starting point, it takes: Time taken by the third car to reach the farthest point = Distance / Speed = 96 m / 18 m/s = 5.33 s

Now, let's calculate the time intervals between the start of each pair of cars.

- Time interval between the start of the first and second cars: Time interval = Time taken by the second car - Time taken by the first car = 2 s - 0 s = 2 s

- Time interval between the start of the first and third cars: Time interval = Time taken by the third car - Time taken by the first car = 5.33 s - 0 s = 5.33 s

- Time interval between the start of the second and third cars: Time interval = Time taken by the third car - Time taken by the second car = 5.33 s - 2 s = 3.33 s

Therefore, the maximum time interval between the start of any two cars is 5.33 seconds.

Answer

The maximum time interval between the start of any two of these three cars from the same point, assuming they all return to the same point at the same time, is 5.33 seconds.