Question

Дорога между двумя пунктами разделена на три участка равной длины. Автомобиль шёл на первом участке со скоростью 60 км/ч, на втором — со скоростью 40 км/ч, а на третьем — со скоростью, равной средней скорости движения на двух первых участках пути. Какова средняя скорость движения на всём пути из одного пункта в другой?

Answer 1

$AB=3x \\ v_{AM}=60km/h \\ v_{MN}=40km/h \\ v_{NB}=? \\ v_{NM}= \frac{2}{ \frac{1}{v_{AM}}+ \frac{1}{v_{MN}} }= \frac{4800}{100} = 48km/h \\ v=48km/h$

Answer 2

Calculating Average Speed for the Entire Journey

To calculate the average speed for the entire journey, we can use the formula:

Average Speed = Total Distance / Total Time

Let's break down the journey into three segments and calculate the average speed for each segment.

1. First Segment: - Speed: 60 km/h - Distance: Let's denote the distance for the first segment as d.

2. Second Segment: - Speed: 40 km/h - Distance: Also d.

3. Third Segment: - Speed: Unknown - Distance: Again d.

Calculating Total Time Taken

We can calculate the total time taken for the journey by adding the time taken for each segment.

1. First Segment: - Time taken = Distance / Speed = d / 60

2. Second Segment: - Time taken = Distance / Speed = d / 40

3. Third Segment: - Time taken = Distance / Speed = d / x (where x is the speed for the third segment)

Adding these times together gives us the total time taken for the journey.

Finding the Average Speed for the Entire Journey

Now, we can use the formula for average speed to find the average speed for the entire journey.

Average Speed = Total Distance / Total Time

Given that the total distance is 3d (as there are three equal segments), and the total time is the sum of the times calculated for each segment, we can find the average speed.

Conclusion

The average speed for the entire journey can be calculated using the above method. If you have the specific value of d, we can proceed with the calculations to find the average speed.