Question

4. Мотоцикліст рухався першу третину шляху зі швидкістю 40 км/год. Другу третину шляху зі швидкістю на 30% більше, ніж на першій ділянці. Останню частину він проїхав зі швидкістю що на 30% Перевищувала середню швидкість на перших двох відрізках. Знайти середню швидкість руху мотоцикліста на всьому шляху.​

Answer 1

To find the average speed of the motorcyclist for the entire journey, we need to calculate the total distance traveled and the total time taken. Let's break down the problem step by step.

Step 1: Calculate the distances for each segment

The motorcyclist traveled the entire distance in three segments: the first third, the second third, and the last part. Let's denote the total distance as "D".

- The first third of the distance: D/3 - The second third of the distance: D/3 - The last part of the distance: D/3

Step 2: Calculate the time taken for each segment

To calculate the time taken, we need to divide the distance by the speed for each segment.

- Time taken for the first third: (D/3) / 40 km/h - Time taken for the second third: (D/3) / (1.3 * 40 km/h) (since the speed is 30% higher than the first segment) - Time taken for the last part: (D/3) / (1.3 * 1.3 * 40 km/h) (since the speed is 30% higher than the average of the first two segments)

Step 3: Calculate the total time taken

The total time taken is the sum of the times taken for each segment.

- Total time taken: Time taken for the first third + Time taken for the second third + Time taken for the last part

Step 4: Calculate the average speed

The average speed is the total distance divided by the total time taken.

- Average speed: Total distance / Total time taken

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

Step 1: Calculate the distances for each segment The motorcyclist traveled the entire distance in three segments: the first third, the second third, and the last part. Let's denote the total distance as "D".

- The first third of the distance: D/3 - The second third of the distance: D/3 - The last part of the distance: D/3

Step 2: Calculate the time taken for each segment To calculate the time taken, we need to divide the distance by the speed for each segment.

- Time taken for the first third: (D/3) / 40 km/h - Time taken for the second third: (D/3) / (1.3 * 40 km/h) (since the speed is 30% higher than the first segment) - Time taken for the last part: (D/3) / (1.3 * 1.3 * 40 km/h) (since the speed is 30% higher than the average of the first two segments)

Step 3: Calculate the total time taken The total time taken is the sum of the times taken for each segment.

- Total time taken: Time taken for the first third + Time taken for the second third + Time taken for the last part

Step 4: Calculate the average speed The average speed is the total distance divided by the total time taken.

- Average speed: Total distance / Total time taken

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

The motorcyclist traveled the first third of the distance at a speed of 40 km/h. The second third of the distance was covered at a speed 30% higher than the first segment, which is 40 km/h * 1.3 = 52 km/h. The last part of the distance was covered at a speed 30% higher than the average of the first two segments, which is 40 km/h * 1.3 * 1.3 = 67.6 km/h.

To find the average speed, we need to calculate the total distance and the total time taken.

- Total distance: D = (D/3) + (D/3) + (D/3) = D - Total time taken: Time taken for the first third + Time taken for the second third + Time taken for the last part

Let's calculate the total time taken:

- Time taken for the first third: (D/3) / 40 km/h = D / (3 * 40) = D / 120 - Time taken for the second third: (D/3) / 52 km/h = D / (3 * 52) = D / 156 - Time taken for the last part: (D/3) / 67.6 km/h = D / (3 * 67.6) = D / 202.8

The total time taken is the sum of the times taken for each segment:

- Total time taken: D / 120 + D / 156 + D / 202.8

Now, we can calculate the average speed:

- Average speed: Total distance / Total time taken = D / (D / 120 + D / 156 + D / 202.8)

Simplifying the expression:

- Average speed: 1 / (1 / 120 + 1 / 156 + 1 / 202.8)

Using a calculator, we can find the average speed of the motorcyclist on the entire journey.