Question

Автомобиль первую половину пути ехал со скоростью в 1.5 раза больше чем вторую половину.найти отношение средней скорости автомобиля на всем пути к скорости на второй половине пути

Answer 1

T1  время затраченное на первую половину 
v1 = S/2t1               t1 = S/2v1
t2 время затраченное на вторую половину
v2 = S/2t2               t2 = S/2v2     

v1 = 1.5v2         v2 = 2v1/3

<v> = S/ (t1+t2)  =  S / (S/3v2    +  S/2v2) = 6v2/5   средняя скорость

<v>/v2 = 6/5 = 1.2

Answer 2

Problem Analysis

We are given that a car traveled the first half of the distance at a speed 1.5 times greater than the speed during the second half. We need to find the ratio of the average speed of the car for the entire journey to the speed during the second half of the journey.

Solution

Let's assume the speed during the second half of the journey is v. According to the given information, the speed during the first half of the journey is 1.5v.

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

Average Speed = Total Distance / Total Time

Since the distance traveled during the first half is the same as the distance traveled during the second half, we can simplify the formula to:

Average Speed = 2 * Distance / Total Time

To find the total time, we need to consider the time taken for the first half and the time taken for the second half.

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

The time taken for the first half is d / (1.5v), and the time taken for the second half is d / v.

Substituting these values into the formula for average speed, we get:

Average Speed = 2d / (d / (1.5v) + d / v)

Simplifying further:

Average Speed = 2 / (1 / (1.5v) + 1 / v)

To find the ratio of the average speed to the speed during the second half, we divide the average speed by v:

Ratio = Average Speed / v = (2 / (1 / (1.5v) + 1 / v)) / v

Simplifying further:

Ratio = 2 / (1 / (1.5v) + 1 / v)

Now we can substitute the value of v to find the ratio.

Calculation

Let's assume the speed during the second half of the journey is v = 60 km/h.

Substituting this value into the formula for the ratio, we get:

Ratio = 2 / (1 / (1.5 * 60) + 1 / 60)

Simplifying further:

Ratio = 2 / (1 / 90 + 1 / 60)

Calculating the values inside the parentheses:

Ratio = 2 / (0.0111 + 0.0167)

Ratio = 2 / 0.0278

Ratio ≈ 71.86

Therefore, the ratio of the average speed of the car for the entire journey to the speed during the second half of the journey is approximately 71.86.

Answer

The ratio of the average speed of the car for the entire journey to the speed during the second half of the journey is approximately 71.86.