Question

На первой половине пути автомобиль движется со скоростью в 4 раза большей, чем на второй. Определите скорости v1, v2 автомобиля на каждом участке, если средняя скорость автомобиля =32км/ч.

Answer 1

(V1+V2)/2=32км/ч
V1+V2=64км/ч
4x+x=64км/ч
5x=64км/ч
Скорость в первой половине: 51,2км/ч
Скорость в второй половине:12,8км/ч

Answer 2

Problem Analysis

We are given that a car travels at a speed four times greater on the first half of the journey compared to the second half. We need to determine the speeds of the car on each segment if the average speed of the car is 32 km/h.

Solution

Let's assume the speed of the car on the first half of the journey is v1 and the speed on the second half is v2. We are also given that the average speed of the car is 32 km/h.

To solve this problem, we can use the formula for average speed:

Average Speed = Total Distance / Total Time

Since the car travels the same distance on both halves of the journey, the total distance is the same for both segments. Therefore, we can write:

Total Distance = Distance on First Half + Distance on Second Half

Let's assume the distance on each half is d. Therefore, the total distance is 2d.

Now, let's calculate the time taken for each segment:

Time on First Half = Distance on First Half / Speed on First Half

Time on Second Half = Distance on Second Half / Speed on Second Half

Since the car travels at a speed four times greater on the first half compared to the second half, we can write:

Speed on First Half = 4 * Speed on Second Half

Substituting the values in the time equations, we get:

Time on First Half = d / v1

Time on Second Half = d / v2

Now, let's substitute the values in the average speed equation:

32 = (2d) / (d/v1 + d/v2)

Simplifying the equation, we get:

32 = 2 / (1/v1 + 1/v2)

To solve this equation, we need to find the values of v1 and v2 that satisfy the equation.

Solution Steps

1. Substitute the given values into the equation: 32 = 2 / (1/v1 + 1/v2) 2. Simplify the equation. 3. Solve the equation to find the values of v1 and v2.

Let's solve the equation to find the values of v1 and v2.

Solution

Substituting the given values into the equation: 32 = 2 / (1/v1 + 1/v2), we get:

32 = 2 / (1/v1 + 1/v2)

Simplifying the equation, we get:

32 = 2v1v2 / (v1 + v2)

Multiplying both sides of the equation by (v1 + v2), we get:

32(v1 + v2) = 2v1v2

Expanding the equation, we get:

32v1 + 32v2 = 2v1v2

Rearranging the equation, we get:

2v1v2 - 32v1 - 32v2 = 0

Factoring the equation, we get:

2(v1 - 16)(v2 - 16) = 0

From this equation, we can see that either v1 - 16 = 0 or v2 - 16 = 0.

If v1 - 16 = 0, then v1 = 16.

If v2 - 16 = 0, then v2 = 16.

Therefore, the possible values for v1 and v2 are 16.

So, the speeds of the car on each segment are 16 km/h.

Answer

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