Question

Два автомобиля выехали на 990 километровую пробежку.первый ехал на 9 км быстрее ,чем втрой и приехал на 1 час раньше второго.найти скорость первого

Answer 1

                                             Скорость              Время                    Расстояние
1 авт.                                        x                             990/x                            990
2 авт.                                    x - 9                          990/(x - 9)                  990

990/(x - 9)  - 990/x = 1
990x - 990x + 8910 = x² - 9x
x² - 9x - 8910 = 0
D = 81 + 35640 = 35721 = 189²
x = (9 + 189) /2 = 99                x = (9 - 189)/2 = -  90  не подх.
Ответ: 99 км.ч

Answer 2

Problem Analysis

We are given that two cars went on a 990-kilometer run. The first car traveled 9 km faster than the second car and arrived 1 hour earlier than the second car. We need to find the speed of the first car.

Solution

Let's assume the speed of the second car is x km/h. Since the first car traveled 9 km faster, its speed will be x + 9 km/h.

We can use the formula distance = speed × time to find the time taken by each car to complete the run.

For the second car: - Distance = 990 km - Speed = x km/h - Time = 990 / x hours

For the first car: - Distance = 990 km - Speed = x + 9 km/h - Time = 990 / (x + 9) hours

We are given that the first car arrived 1 hour earlier than the second car. So, we can set up the equation:

990 / x - 990 / (x + 9) = 1

To solve this equation, we can multiply both sides by x(x + 9) to eliminate the denominators:

990(x + 9) - 990x = x(x + 9)

Simplifying the equation:

990x + 8910 - 990x = x^2 + 9x

8910 = x^2 + 9x

Rearranging the equation:

x^2 + 9x - 8910 = 0

Now we can solve this quadratic equation to find the value of x.

Let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 9, and c = -8910.

Plugging in the values:

x = (-9 ± √(9^2 - 4 * 1 * -8910)) / (2 * 1)

Simplifying further:

x = (-9 ± √(81 + 35640)) / 2

x = (-9 ± √35721) / 2

Calculating the square root of 35721:

√35721 ≈ 189

Now we have two possible values for x:

x = (-9 + 189) / 2 ≈ 90

x = (-9 - 189) / 2 ≈ -99

Since speed cannot be negative, we can discard the value of x = -99.

Therefore, the speed of the second car (x) is approximately 90 km/h.

The speed of the first car is x + 9, which is approximately 99 km/h.

Answer

The speed of the first car is approximately 99 km/h.