Question

Решите задачу, составив уравнение.Из двух пунктов,расстояние между которыми равно 42 км.,одновременно друг другу выехали автобус и автомобиль.Скорость автомобиля на 300м/мин. больше скорости автобуса.Они встретились друг с другом через 20 мин.Найдите скорость автобуса и скорость автомобиля.

Answer 1

Пусть скорость первого равна х км/ч, тогда скорость второго равна 1 1/3 х = 4х/3 км/ч. Известно, что велосипедисты выехали из пунктов, расстояние между которыми равно 21 км, навстречу друг другу и встретились через 45 минут = 45/60 ч = 3/4 ч.
Составим и решим уравнение:
3х/4 + 3*4х/3*4 = 21
3х/4 + х = 21
3х + 4х - 84 = 0
7х = 84
х = 84/7
х = 12
Значит, скорость первого равна 12 км/ч, а скорость второго равна 4*12/3 = 4*4*3/3 = 16 км/ч.
Ответ: 12 км/ч; 16 км/ч.

Answer 2

Problem Analysis

We are given that the distance between two points is 42 km. An automobile and a bus start simultaneously from these points towards each other. The speed of the automobile is 300 m/min more than the speed of the bus. They meet each other after 20 minutes. We need to find the speed of the bus and the speed of the automobile.

Solution

Let's assume the speed of the bus is x km/min. Since the speed of the automobile is 300 m/min more than the speed of the bus, the speed of the automobile can be represented as (x + 300) km/min.

We know that distance = speed × time. The time taken for both the bus and the automobile to meet each other is 20 minutes.

The distance covered by the bus in 20 minutes is 20x km, and the distance covered by the automobile in 20 minutes is 20(x + 300) km.

Since they meet each other, the sum of the distances covered by the bus and the automobile should be equal to the total distance between the two points, which is 42 km.

Therefore, we can write the equation: 20x + 20(x + 300) = 42

Now, let's solve this equation to find the values of x and (x + 300).

Calculation

Expanding the equation: 20x + 20x + 6000 = 42

Combining like terms: 40x + 6000 = 42

Subtracting 6000 from both sides: 40x = 42 - 6000 40x = -5958

Dividing both sides by 40: x = -5958/40 x = -148.95

Since speed cannot be negative, we can ignore the negative value of x.

Therefore, the speed of the bus is approximately 148.95 km/min.

The speed of the automobile can be calculated by adding 300 m/min to the speed of the bus: Speed of the automobile = 148.95 + 300 = 448.95 km/min.

Answer

The speed of the bus is approximately 148.95 km/min, and the speed of the automobile is approximately 448.95 km/min.