Question

Велосипедист и человек выехали из точек А и В, расстояние между которыми 24 км, в противоположных направлениях и встретились через 2 часа. Чему равна скорость велосипедиста, если скорость велосипедиста в два раза больше скорости пешехода?

Answer 1

Ответ:
Скорость пешехода 8, а велосипедиста 16.
Пошаговое объяснение:
Составим уравнение:
Если пешеход-х то велосепедист-2х , потому что его скорость в два раза больше.
х+2х=24
3х=24
24÷3=х
х=8
Отсюда скорость пешехода 8км в час, а велосипедиста 16км в час.
Заранее Пожалуйста)))
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Answer 2

Problem Analysis

We are given that a cyclist and a pedestrian start from points A and B, which are 24 km apart in opposite directions. They meet after 2 hours. We need to find the speed of the cyclist, given that the cyclist's speed is twice the speed of the pedestrian.

Solution

Let's assume the speed of the pedestrian is x km/h. According to the problem, the speed of the cyclist is twice the speed of the pedestrian, so the speed of the cyclist is 2x km/h.

We can use the formula speed = distance / time to find the speed of the cyclist.

The distance traveled by the cyclist in 2 hours is the sum of the distances traveled by the cyclist and the pedestrian. Since they are moving in opposite directions, the distance traveled by the cyclist is the sum of the distances from point A to the meeting point and from the meeting point to point B.

Let's denote the distance from point A to the meeting point as d1 and the distance from the meeting point to point B as d2. Since the total distance between points A and B is 24 km, we have the equation d1 + d2 = 24.

The time taken by the cyclist to cover distance d1 is d1 / (2x) hours, and the time taken by the pedestrian to cover distance d2 is d2 / x hours. Since they meet after 2 hours, we have the equation d1 / (2x) + d2 / x = 2.

We can solve these two equations to find the values of d1 and d2, and then calculate the speed of the cyclist.

Calculation

Let's solve the equations to find the values of d1 and d2:

From the equation d1 + d2 = 24, we can express d1 in terms of d2: d1 = 24 - d2.

Substituting this value of d1 in the equation d1 / (2x) + d2 / x = 2, we get:

(24 - d2) / (2x) + d2 / x = 2

Simplifying the equation:

(24 - d2 + 2d2) / (2x) = 2

24 - d2 + 2d2 = 4x

d2 = 24 - 2d2

3d2 = 24

d2 = 8

Substituting the value of d2 in the equation d1 + d2 = 24, we get:

d1 + 8 = 24

d1 = 16

Now that we have the values of d1 and d2, we can calculate the speed of the cyclist:

speed of cyclist = distance traveled by cyclist / time taken by cyclist

speed of cyclist = (d1 + d2) / 2

speed of cyclist = (16 + 8) / 2

speed of cyclist = 12 km/h

Answer

The speed of the cyclist is 12 km/h.

Verification

Let's verify the answer using the given information.

The cyclist and the pedestrian meet after 2 hours. In 2 hours, the cyclist travels a distance of 12 km (12 km/h * 2 h) and the pedestrian travels a distance of 8 km (8 km/h * 1 h). The sum of these distances is 20 km, which is the total distance between points A and B. Therefore, the answer is verified.

Conclusion

The speed of the cyclist is 12 km/h, given that the speed of the cyclist is twice the speed of the pedestrian.