Question

Весь путь автомобиля составил 465 км. На первый участок пути по шоссе автомобиль затратил 3ч, на второй по проселочной дороге - 5ч. Найдите скорость автомобиль на каждом участке пути, если известно, что на проселочной дороге его скорость была на 27 км\ч меньше, чем на шоссе.

Answer 1

Весь путь 465, в том числе три часа по шоссе и пять по проселкам...

Answer 2

Problem Analysis

We are given that the total distance traveled by a car is 465 km. The car took 3 hours to travel the first part of the journey on a highway and 5 hours to travel the second part on a dirt road. We also know that the car's speed on the dirt road was 27 km/h less than its speed on the highway. We need to find the speed of the car on each part of the journey.

Solution

Let's assume the speed of the car on the highway is x km/h. Since the car's speed on the dirt road is 27 km/h less than its speed on the highway, the speed on the dirt road would be x - 27 km/h.

We can use the formula speed = distance / time to find the speed of the car on each part of the journey.

# Speed on the Highway

The distance traveled on the highway is not given, but we can calculate it using the time and the speed on the highway. We know that the car took 3 hours to travel the first part of the journey on the highway. Therefore, the distance traveled on the highway can be calculated as follows:

distance on the highway = speed on the highway * time on the highway

Substituting the values, we get:

distance on the highway = x km/h * 3 h

# Speed on the Dirt Road

Similarly, we can calculate the distance traveled on the dirt road using the time and the speed on the dirt road. We know that the car took 5 hours to travel the second part of the journey on the dirt road. Therefore, the distance traveled on the dirt road can be calculated as follows:

distance on the dirt road = speed on the dirt road * time on the dirt road

Substituting the values, we get:

distance on the dirt road = (x - 27) km/h * 5 h

# Total Distance

We are given that the total distance traveled by the car is 465 km. Therefore, the sum of the distances traveled on the highway and the dirt road should be equal to 465 km:

distance on the highway + distance on the dirt road = 465 km

Substituting the calculated values, we get:

(x km/h * 3 h) + ((x - 27) km/h * 5 h) = 465 km

Now we can solve this equation to find the value of x, which represents the speed of the car on the highway.

Calculation

Let's solve the equation to find the value of x:

(x km/h * 3 h) + ((x - 27) km/h * 5 h) = 465 km

Simplifying the equation:

3x + 5(x - 27) = 465

Expanding and simplifying further:

3x + 5x - 135 = 465

8x - 135 = 465

8x = 600

x = 75

Therefore, the speed of the car on the highway is 75 km/h.

Since the speed on the dirt road is 27 km/h less than the speed on the highway, the speed on the dirt road would be:

75 km/h - 27 km/h = 48 km/h

Therefore, the speed of the car on the dirt road is 48 km/h.

Answer

The speed of the car on the highway is 75 km/h and the speed of the car on the dirt road is 48 km/h.

Note: The sources provided do not contain relevant information for this specific problem.

Answer 3

Пусть скорость автомобиля на первом участке пути по шоссе равна V км/ч, а на втором участке по проселочной дороге - (V-27) км/ч.

Тогда время, затраченное на первый участок пути, равно 3 часа, а на второй - 5 часов.

Мы знаем, что расстояние равно скорость умноженная на время. Таким образом, на первом участке пути расстояние равно 3V км, а на втором участке - 5(V-27) км.

Итак, всего путь составил 465 км, поэтому:

3V + 5(V-27) = 465

Раскрываем скобки:

3V + 5V - 135 = 465

Складываем подобные члены:

8V - 135 = 465

Прибавляем 135 к обеим сторонам уравнения:

8V = 600

Делим обе стороны на 8:

V = 75

Таким образом, скорость автомобиля на первом участке пути (по шоссе) равна 75 км/ч, а на втором участке (по проселочной дороге) - 75-27=48 км/ч.