Question

Помогите плиииз Проехав 3 часа по грунтовой дороге и 0,5 часа о асфальтовой дороге мотоциклист проехал 110 км пути. Скорость мотоциклиста по асфальтовой дороге на 10 км/час больше его скорости на грунтовой дороге. Найдите скорости мотоциклиста на грунтовой и на асфальтовой дорогах.

Answer 1

х - скорость на грунтовой дороге,  (х+10) - скорость на асфальтовой дороге

3х + 0,5(х + 10) = 110

3х + 0,5х + 5 = 110

3,5х = 110 - 5

х = 105 : 3,5

х = 30 (км/ч) - скорость на грунтовке

30 + 10 = 40 (км/ч) - скорость на асфальте

Проверка: 3*30 + 0,5*40 = 90 + 20 = 110 (км)

Answer 2

Problem Analysis

We are given that a motorcyclist traveled for 3 hours on a dirt road and 0.5 hours on an asphalt road, covering a total distance of 110 km. The speed of the motorcyclist on the asphalt road is 10 km/h faster than their speed on the dirt road. We need to find the speeds of the motorcyclist on both types of roads.

Solution

Let's assume the speed of the motorcyclist on the dirt road is x km/h. According to the problem, the speed on the asphalt road is 10 km/h faster, so the speed on the asphalt road is x + 10 km/h.

We can use the formula distance = speed × time to calculate the distances traveled on each type of road.

On the dirt road: - Speed = x km/h - Time = 3 hours - Distance = x × 3 km

On the asphalt road: - Speed = x + 10 km/h - Time = 0.5 hours - Distance = (x + 10) × 0.5 km

The total distance traveled is given as 110 km. Therefore, we can write the equation:

x × 3 + (x + 10) × 0.5 = 110

Now, let's solve this equation to find the value of x.

Calculation

3x + 0.5(x + 10) = 110

Simplifying the equation:

3x + 0.5x + 5 = 110

Combining like terms:

3.5x + 5 = 110

Subtracting 5 from both sides:

3.5x = 105

Dividing both sides by 3.5:

x = 30

Answer

The speed of the motorcyclist on the dirt road is 30 km/h and the speed on the asphalt road is 40 km/h.

Please let me know if I can help you with anything else.