Question

Дам 35 баллов!Из пункта А в пункт Б расстояние между которыми 2 км выехали два автомобиля. Так как скорость первого автомобиля на 4 км в час больше скорости второго то первый автомобиль в пункт назначения прибыл на 15 раньше чем второй.Найдите скорость каждого из автомобилей .

Answer 1

Вот смотри фотку  там все есть 

Answer 2

Problem Analysis

We are given that two cars traveled from point A to point B, with a distance of 2 km between them. The first car arrived at the destination 15 minutes earlier than the second car because its speed was 4 km/h faster than the speed of the second car. We need to find the speed of each car.

Solution

Let's assume the speed of the second car is x km/h. Since the speed of the first car is 4 km/h faster, its speed will be x + 4 km/h.

We can use the formula speed = distance / time to find the time taken by each car to travel from point A to point B.

For the first car: - Speed = x + 4 km/h - Distance = 2 km - Time = Distance / Speed = 2 / (x + 4) hours

For the second car: - Speed = x km/h - Distance = 2 km - Time = Distance / Speed = 2 / x hours

According to the given information, the first car arrived 15 minutes earlier than the second car. Since 1 hour is equal to 60 minutes, 15 minutes is equal to 15/60 = 1/4 hour.

So, the time taken by the first car is 1/4 hour less than the time taken by the second car.

Setting up the equation: Time taken by the first car = Time taken by the second car - 1/4

2 / (x + 4) = 2 / x - 1/4

To solve this equation, we can cross-multiply and simplify:

2x = 2(x + 4) - (1/4)(x)(x + 4)

2x = 2x + 8 - (1/4)(x^2 + 4x)

2x = 2x + 8 - (1/4)x^2 - x

0 = 8 - (1/4)x^2 - x

Rearranging the equation: (1/4)x^2 + x - 8 = 0

Now we can solve this quadratic equation to find the value of x, which represents the speed of the second car.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case: a = 1/4, b = 1, c = -8

Substituting the values into the quadratic formula: x = (-(1) ± √((1)^2 - 4(1/4)(-8))) / (2(1/4))

Simplifying: x = (-1 ± √(1 + 8)) / (1/2)

x = (-1 ± √9) / (1/2)

x = (-1 ± 3) / (1/2)

We have two possible solutions: 1. x = (-1 + 3) / (1/2) = 2 / (1/2) = 2 * 2 = 4 km/h 2. x = (-1 - 3) / (1/2) = -4 / (1/2) = -4 * 2 = -8 km/h

Since speed cannot be negative, the speed of the second car is 4 km/h.

Now we can find the speed of the first car: Speed of the first car = Speed of the second car + 4 = 4 + 4 = 8 km/h

Answer

The speed of the first car is 8 km/h, and the speed of the second car is 4 km/h.