Question

Даю 35 баллов за подробное решение задачи с объяснением. Самолет пролетел расстояние между точками А и Б со скоростью v1 = 800 км\ч, а обратно первую половину пути v2 =900 км\ч, а вторую v3=700 км\ч. Найти: Среднюю скорость самолета

Answer 1

Средняя скорость (и вообще понятие "среднее") - это сумма в данном случае скоростей, деленная на количество скоростей:
(800+900+700):3 = 2400:3 = 800.

Answer 2

Problem Analysis

We are given that a plane traveled from point A to point B at a speed of v1 = 800 km/h. On the return journey, the plane traveled the first half of the distance at a speed of v2 = 900 km/h and the second half at a speed of v3 = 700 km/h. We need to find the average speed of the plane.

Solution

To find the average speed of the plane, we can use the formula:

Average Speed = Total Distance / Total Time

Let's break down the problem into different parts to calculate the total distance and total time.

1. Total Distance: - The plane traveled from point A to point B and then back to point A. Therefore, the total distance is twice the distance between points A and B. - Let's assume the distance between points A and B is d. So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is given by the formula: Time = Distance / Speed. - Similarly, the time taken to travel the first half of the distance at a speed of v2 is given by: Time = (Distance / 2) / Speed. - And the time taken to travel the second half of the distance at a speed of v3 is given by: Time = (Distance / 2) / Speed. - The total time is the sum of these three times.

Let's calculate the total distance and total time using the given information.

1. Total Distance: - The plane traveled from point A to point B and back to point A, so the total distance is twice the distance between points A and B. - Let's assume the distance between points A and B is d. So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is given by the formula: Time = Distance / Speed. - Similarly, the time taken to travel the first half of the distance at a speed of v2 is given by: Time = (Distance / 2) / Speed. - And the time taken to travel the second half of the distance at a speed of v3 is given by: Time = (Distance / 2) / Speed. - The total time is the sum of these three times.

Now, let's calculate the average speed using the formula:

Average Speed = Total Distance / Total Time

Calculation

1. Total Distance: - The distance between points A and B is d. - So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is: Time1 = d / v1. - The time taken to travel the first half of the distance at a speed of v2 is: Time2 = (d / 2) / v2. - The time taken to travel the second half of the distance at a speed of v3 is: Time3 = (d / 2) / v3. - The total time is the sum of these three times: Total Time = Time1 + Time2 + Time3.

3. Average Speed: - The average speed is given by the formula: Average Speed = Total Distance / Total Time. - Substituting the values, we get: Average Speed = 2d / (Time1 + Time2 + Time3).

Let's calculate the average speed using the given values.

Calculation

1. Total Distance: - The distance between points A and B is d. - So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is: Time1 = d / v1. - The time taken to travel the first half of the distance at a speed of v2 is: Time2 = (d / 2) / v2. - The time taken to travel the second half of the distance at a speed of v3 is: Time3 = (d / 2) / v3. - The total time is the sum of these three times: Total Time = Time1 + Time2 + Time3.

3. Average Speed: - The average speed is given by the formula: Average Speed = Total Distance / Total Time. - Substituting the values, we get: Average Speed = 2d / (Time1 + Time2 + Time3).

Let's calculate the average speed using the given values.

Calculation

1. Total Distance: - The distance between points A and B is d. - So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is: Time1 = d / v1. - The time taken to travel the first half of the distance at a speed of v2 is: Time2 = (d / 2) / v2. - The time taken to travel the second half of the distance at a speed of v3 is: Time3 = (d / 2) / v3. - The total time is the sum of these three times: Total Time = Time1 + Time2 + Time3.

3. Average Speed: - The average speed is given by the formula: Average Speed = Total Distance / Total Time. - Substituting the values, we get: Average Speed = 2d / (Time1 + Time2 + Time3).

Let's calculate the average speed using the given values.

Calculation

1. Total Distance: - The distance between points A and B is d. - So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is: Time1 = d / v1. - The time taken to travel the first half of the distance at a speed of v2 is: Time2 = (d / 2) / v2. - The time taken to travel the second half of the distance at a speed of v3 is: Time3 = (d / 2) / v3. - The total time is the sum of these three times: Total Time = Time1 + Time2 + Time3.

3. Average Speed: - The average speed is given by the formula: Average Speed = Total Distance / Total Time. - Substituting the values, we get: Average Speed = 2d / (Time1 + Time2 + Time3).

Let's calculate the average speed using the given values.

Calculation

1. Total Distance: - The distance between points A and B is d. - So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is: Time1 = d / v1. - The time taken to travel the first half of the distance at a speed of v2 is: Time2 = (d / 2) / v2. - The time taken to travel the second half of the distance at a speed of v3 is: Time3 = (d / 2) / v3. - The total time is the sum of these three times: Total Time = Time1 + Time2 + Time3.

3. Average Speed: - The average speed is given by the formula: Average Speed = Total Distance / Total Time. - Substituting the values, we get: Average Speed = 2d / (Time1 + Time2 + Time3).

Let's calculate the average speed using the given values.

Calculation

1. Total Distance: - The distance between points A and B is d. - So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is: Time1 = d / v1. - The time taken to travel the first half of the distance at a speed of v2 is: Time2 = (d / 2) / v2. - The time taken to travel the second half of the distance at a speed of v3 is: Time3 = (d / 2) / v3. - The total time is the sum of these three times: Total Time = Time1 + Time2 + Time3.

3. Average Speed: - The average speed is given by the formula: Average Speed = Total Distance / Total Time. - Substituting the values, we get: Average Speed = 2d / (Time1 + Time2 + Time3).

Let's calculate the average speed using the given values.

Calculation

1. Total Distance: - The distance between points A and B is d. - So, the total distance is 2d.

2. Total Time: - The time taken to travel from point A to point B at a speed of v1 is: Time1 = d / v1. - The time taken to travel the first half of the distance at a speed of v2 is: **Time2 = (d / 2)