Question

Автомобиль выехал из пункта а в пункт в и некоторое время двигался с постоянной скоростью. проехав 3/4 пути,он увеличил скорость на 20 км/ч. когда автомобиль прибыл в пункт В,оказалось,что его средняя скорость движения составила 64 км/ч.найдитепервоначальную скорость автомобиля

Answer 1

 х км/ч начальная скорость 

расстояние 1 (еденица) 

 

3/4х+1/4(х+20)=64*1

3/4х+1/4х+5=64

х=59 км/ч 

 

Проверка

3/4*59+1/4*79= 256/4=64

 

Answer 2

Problem Analysis

We are given that a car traveled from point A to point B at a constant speed. After covering 3/4 of the distance, the car increased its speed by 20 km/h. When the car arrived at point B, its average speed was 64 km/h. We need to find the initial speed of the car.

Solution

Let's assume the total distance from point A to point B is D km.

We know that the car traveled 3/4 of the distance, which is (3/4)D km, at its initial speed.

After covering (3/4)D km, the car increased its speed by 20 km/h.

The remaining distance from that point to point B is (1/4)D km.

We can calculate the time taken to cover this remaining distance using the average speed formula: Average speed = Total distance / Total time.

We can rearrange this formula to find the total time taken: Total time = Total distance / Average speed.

Let's calculate the total time taken to cover the remaining distance: Total time = (1/4)D / 64.

We can also calculate the time taken to cover the initial distance at the initial speed: Time taken = (3/4)D / (Initial speed).

Since the car traveled at a constant speed, the time taken to cover the initial distance and the time taken to cover the remaining distance should be the same.

Setting the two equations equal to each other, we can solve for the initial speed of the car.

Let's calculate the initial speed using the given information.

Calculation

Let's assume the total distance from point A to point B is D km.

The car traveled 3/4 of the distance, so the distance covered is (3/4)D km.

The remaining distance is (1/4)D km.

Using the average speed formula, we can calculate the total time taken to cover the remaining distance: Total time = (1/4)D / 64.

The time taken to cover the initial distance is the same: Time taken = (3/4)D / (Initial speed).

Setting the two equations equal to each other, we have: (1/4)D / 64 = (3/4)D / (Initial speed).

Simplifying the equation, we get: 1 / 64 = 3 / (4 * Initial speed).

Cross-multiplying, we have: Initial speed = (4 * 3) / (1 * 64).

Calculating the initial speed, we get: Initial speed = 12 / 64.

Simplifying further, we find: Initial speed = 0.1875 km/h.

Therefore, the initial speed of the car was 0.1875 km/h.

Answer

The initial speed of the car was 0.1875 km/h.

Explanation

The car traveled from point A to point B at a constant speed. After covering 3/4 of the distance, the car increased its speed by 20 km/h. When the car arrived at point B, its average speed was 64 km/h. By setting the time taken to cover the initial distance equal to the time taken to cover the remaining distance, we can solve for the initial speed of the car. The initial speed of the car was calculated to be 0.1875 km/h.