Question

Поезд прошел четыре участка пути относящиеся как 1:3:4:2 , за времена которые относились как 2:4:3:1. Движение на всех участках равномерное. скорость на последнем v=80 км\час Найдите среднюю скорость на всем пути.

Answer 1

Поезд прошел расстояние S, состоящее из 4 участков пути S₁:S₂:S₃:S₄=1:3:4:2. 
Это значит, что S₁=S/10, S₂=3S/10, S₃=4S/10, S₄=2S/10.
Аналогично и время: все время t состояло из 4 периодов t₁:t₂:t₃:t₄=2:4:3:1.
Это значит, что t₁=2t/10, t₂=4t/10, t₃=3t/10, t₄=t/10.
По условию v₄=80 км/ч, значит v₄ =S₄:t₄=2S/10 : t/10=2S/t или S/t=40

Vcp=(S₁+S₂+S₃+S₄) : (t₁+t₂+t₃+t₄)=S/10(1+3+4+2) : t/10(2+4+3+1)=S/t=40 км/ч

Answer 2

Problem Analysis

We are given that a train has traveled four segments of a journey, with time ratios of 1:3:4:2. The corresponding time ratios for these segments are 2:4:3:1. The train is moving at a constant speed of 80 km/h on the last segment. We need to find the average speed of the train for the entire journey.

Solution

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

Let's assume that the distances for the four segments are d1, d2, d3, and d4, respectively.

Since the train is moving at a constant speed, we can use the formula: speed = distance / time.

Let's calculate the distances for each segment using the given time ratios:

- Segment 1: time ratio = 2, distance ratio = 1 - Segment 2: time ratio = 4, distance ratio = 3 - Segment 3: time ratio = 3, distance ratio = 4 - Segment 4: time ratio = 1, distance ratio = 2

Let's assume the distance for segment 1 is d1. Then the distances for the other segments can be calculated as follows:

- Segment 2: d2 = (3/1) * d1 - Segment 3: d3 = (4/3) * d2 - Segment 4: d4 = (2/1) * d3

Now, let's calculate the total distance traveled:

- Total distance = d1 + d2 + d3 + d4

Next, let's calculate the total time taken for the entire journey:

- Total time = (d1 / 80) + (d2 / 80) + (d3 / 80) + (d4 / 80)

Finally, we can calculate the average speed using the formula:

- Average speed = Total distance / Total time

Let's perform the calculations to find the average speed.

Calculation

Let's assume the distance for segment 1 is d1.

- Segment 2: d2 = (3/1) * d1 = 3d1 - Segment 3: d3 = (4/3) * d2 = (4/3) * 3d1 = 4d1 - Segment 4: d4 = (2/1) * d3 = 2 * 4d1 = 8d1

Total distance = d1 + 3d1 + 4d1 + 8d1 = 16d1

Total time = (d1 / 80) + (3d1 / 80) + (4d1 / 80) + (8d1 / 80) = 16d1 / 80 = d1 / 5

Average speed = Total distance / Total time = (16d1) / (d1 / 5) = 80 km/h

Answer

The average speed of the train for the entire journey is 80 km/h.

Note: The specific values for distances (d1, d2, d3, d4) were not provided in the question, so we cannot calculate the exact distance traveled. However, the average speed will always be 80 km/h based on the given time ratios and the speed on the last segment.