Question

Помогите пожалуйста. Первую половину пути велосипедист ехал со скоростьб в 8 раз больше,чем втору половину пути. Средняя скорость на всем участке =16км/ч. Найти среднюю скорость на первом и на втором участке?

Answer 1

Vср=(V1+V2)/2
V1=8V2
Vср= ( 8V2+V2)/2
Vср = 9V2/2= 4,5V2
4,5V2=16км/ч
V2= 16/4,5
V2= 3,5км/ч
V1= 8*3,5=28км/ч

Answer 2

Problem Analysis

We are given that a cyclist traveled the first half of the distance with a speed 8 times greater than the speed at which they traveled the second half. The average speed for the entire journey is 16 km/h. We need to find the average speed for the first and second halves of the journey.

Solution

Let's assume the distance of the entire journey is D km.

We know that the average speed is given by the formula:

Average Speed = Total Distance / Total Time

Since the total distance is D km and the average speed is 16 km/h, we can find the total time taken for the journey:

Total Time = Total Distance / Average Speed

The cyclist traveled the first half of the distance with a speed 8 times greater than the speed at which they traveled the second half. Let's assume the speed for the second half of the journey is x km/h. Therefore, the speed for the first half of the journey is 8x km/h.

The time taken to travel the first half of the journey is D/2 / (8x) hours, and the time taken to travel the second half of the journey is D/2 / x hours.

The total time taken for the journey is the sum of the times taken for the first and second halves:

Total Time = D/2 / (8x) + D/2 / x

Now we can substitute the value of Total Time into the equation for Average Speed:

16 = D / (D/2 / (8x) + D/2 / x)

Simplifying the equation:

16 = D / (D/16x + D/8x)

16 = D / (D(1/16x + 1/8x))

16 = D / (D(2/16x))

16 = D / (D/8x)

16 = 8x

Solving for x:

x = 2

Therefore, the speed for the second half of the journey is 2 km/h, and the speed for the first half of the journey is 8 times greater, which is 8 * 2 = 16 km/h.

Answer

The average speed on the first half of the journey is 16 km/h, and the average speed on the second half of the journey is 2 km/h.