Question

Половину времени движения из одного города в другой автомобиль перемещаться со скоростью 60 км в час. С какой скоростью он двигался во второй половине времени своего пути если средняя скорость автомобиля 65 км в час?

Answer 1

Пусть весь путь-S
Тогда первую половину пути автомобиль проехал за S:2v1
А вторую за S:2v2
Все время- S(v1+v2):2v1v2
S/(S(v1+v2)/2v1v2)=2v1v2/(v1+v2)=2*80*40/(80+40)=6400/120=53. 3 км\ч

Answer 2

Calculation of Average Speed:

To calculate the speed at which the car was moving in the second half of its journey, we can use the formula for average speed:

Average Speed = Total Distance / Total Time

We are given that the car travels at a speed of 60 km/h for the first half of the journey and has an average speed of 65 km/h for the entire journey.

Let's assume that the total distance traveled by the car is D km. Since the car travels at a speed of 60 km/h for the first half of the journey, the time taken for the first half is D / (2 * 60) hours. Similarly, the time taken for the second half of the journey is D / (2 * x) hours, where x is the speed at which the car moves in the second half.

The total time taken for the entire journey is D / 60 hours, and the average speed is given as 65 km/h.

Using the formula for average speed, we can write the equation:

65 = D / (D / (2 * 60) + D / (2 * x))

Simplifying the equation, we get:

65 = 2 * 60 * x / (60 + x)

Now, we can solve this equation to find the value of x, which represents the speed at which the car moves in the second half of its journey.

Solving the Equation:

To solve the equation, we can use algebraic manipulation or numerical methods. Let's use algebraic manipulation to solve it.

Multiplying both sides of the equation by (60 + x), we get:

65 * (60 + x) = 2 * 60 * x

Expanding and simplifying the equation, we have:

3900 + 65x = 120x

Subtracting 65x from both sides, we get:

3900 = 55x

Dividing both sides by 55, we find:

x = 3900 / 55 = 70

Therefore, the car was moving at a speed of 70 km/h in the second half of its journey.

Conclusion:

The car was moving at a speed of 70 km/h in the second half of its journey, given that it traveled at a speed of 60 km/h for the first half and had an average speed of 65 km/h for the entire journey.