Question

Из пункта А и В ,расстояние между которыми равна 290 км , выехали одновременно навстречу друг другу два автомобиля , скорость одного из которых на 5 км/ч больше скорость другого . Через 2 ч автомобили оказались на расстоянии 20 км друг от друга . С какой скоростью ехал каждый автомобиль ? Рассмотрите случаи : а) когда автомобили ещё не встретились; б)когда они уже миновали место встречи.

Answer 1

1 ав.-х+5

2 ав.- х

1)290 - 20= 270 км -проехал первй автомобиль за 2 часа

2)если скорость первого автомобиля х+5 а за 2 часа он проехал 270 км то за час он проедет

270:2=135 км/ч скорость 1 автомобиля

 

Answer 2

Problem Analysis

We have two cars, A and B, that start at points A and B, respectively, and travel towards each other. The distance between points A and B is 290 km. One car is traveling 5 km/h faster than the other. After 2 hours, the cars are 20 km apart. We need to find the speeds of each car in two scenarios: when they haven't met yet and when they have already passed each other.

Scenario A: Cars Haven't Met Yet

Let's assume that the speed of car A is x km/h. Since car B is traveling 5 km/h faster, the speed of car B is (x + 5) km/h.

To find the speeds of the cars, we can use the formula: distance = speed × time.

After 2 hours, car A has traveled a distance of 2x km, and car B has traveled a distance of 2(x + 5) km. The sum of these distances should be equal to the total distance between the cars, which is 290 km.

So, we can set up the equation: 2x + 2(x + 5) = 290.

Simplifying the equation: 2x + 2x + 10 = 290.

Combining like terms: 4x + 10 = 290.

Subtracting 10 from both sides: 4x = 280.

Dividing both sides by 4: x = 70.

Therefore, the speed of car A is 70 km/h, and the speed of car B is (70 + 5) = 75 km/h.

Scenario B: Cars Have Already Passed Each Other

In this scenario, the total distance traveled by both cars is still 290 km. However, the relative distance between them is now 20 km.

Let's assume that car A has traveled a distance of y km. Since car B is traveling 5 km/h faster, car B has traveled a distance of (y + 20) km.

Setting up the equation: y + (y + 20) = 290.

Simplifying the equation: 2y + 20 = 290.

Subtracting 20 from both sides: 2y = 270.

Dividing both sides by 2: y = 135.

Therefore, car A has traveled a distance of 135 km, and car B has traveled a distance of (135 + 20) = 155 km.

Summary of Results

In scenario A, when the cars haven't met yet: - Car A is traveling at a speed of 70 km/h. - Car B is traveling at a speed of 75 km/h.

In scenario B, when the cars have already passed each other: - Car A has traveled a distance of 135 km. - Car B has traveled a distance of 155 km.

Please let me know if you need any further clarification or assistance!