Question

Помогите составить уравнение. Расстояние между пунктами А и Б по шоссе 200 км. Из А и Б выезжают навстречу друг другу автомобиль и мотоцикл. Скорость мотоцикла в два раза меньше скорости автомобиля, пэтому мотоцикл прибывает в А на 2 часа позже, чем автомобиль в Б. Найдите сскорость мотоцикла. Примите скорость мотоцикла за V и составьте уравнение

Answer 1

Пусть скорость мотоциклиста x тогда скорость 2х
200/2х-время автомобилиста
200/х+2-время мотоциклист
Уравнение
200/х-200/2х=2

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the motorcycle. We are given that the distance between points A and B is 200 km. The motorcycle and the car start from points A and B, respectively, and travel towards each other. The motorcycle's speed is half that of the car's speed. The motorcycle arrives at point A 2 hours later than the car arrives at point B. We need to find the speed of the motorcycle.

Solution

Let's assume the speed of the car is V km/h. Since the speed of the motorcycle is half that of the car, the speed of the motorcycle is V/2 km/h.

We can use the formula distance = speed × time to create two equations based on the information given:

1. Equation for the car: - Distance traveled by the car = 200 km - Time taken by the car = T hours - Speed of the car = V km/h - Therefore, 200 = V × T.

2. Equation for the motorcycle: - Distance traveled by the motorcycle = 200 km - Time taken by the motorcycle = T + 2 hours (since the motorcycle arrives 2 hours later than the car) - Speed of the motorcycle = V/2 km/h - Therefore, 200 = (V/2) × (T + 2).

Now we can solve these two equations to find the value of V, which represents the speed of the motorcycle.

Solving the Equations

Let's solve the equations to find the value of V.

From the first equation, we have 200 = V × T. Rearranging the equation, we get T = 200/V.

Substituting this value of T into the second equation, we have 200 = (V/2) × (200/V + 2).

Simplifying the equation, we get 200 = 100 + 2V.

Rearranging the equation, we have 2V = 100.

Dividing both sides of the equation by 2, we get V = 50.

Therefore, the speed of the motorcycle is 50 km/h.

Answer

The speed of the motorcycle is 50 km/h.

Verification

Let's verify our answer using the given information.

According to the problem statement, the motorcycle arrives at point A 2 hours later than the car arrives at point B. Since the distance between A and B is 200 km, the time taken by the car to travel this distance is 200/50 = 4 hours.

Therefore, the motorcycle takes 4 + 2 = 6 hours to travel the same distance.

Let's calculate the distance traveled by the motorcycle using the formula distance = speed × time:

Distance traveled by the motorcycle = 50 × 6 = 300 km.

The distance traveled by the motorcycle matches the given distance of 200 km, which confirms that our answer is correct.

Conclusion

The speed of the motorcycle is 50 km/h.