Question

З міста А до міста В відстань між якими 360 км, одночасно виїхали два автомобілі. швидкість одного з них була на 10 км/год. більшою за швидкість другого, і тому він прибув до пункта призначення на 1/2(дріб) год раніше. Знайдіть швидкість кожного автомобіля.​

Answer 1

Ответ:

80 км/ч

Объяснение:

х- скорость автомобиля, который двигался

медленнее, км/ч. 360/x=360/(x+10) +30/60

360(x+10)-360x=(x(x+10))/2

1x2

720(x+10-x)=x2+10x

подходит по смыслу задачи.

x²+10x-7200=0; D=100+28800=28900 x1=(-10-170)/2=-180/2=-90 - этот корень не 具

x2(-10+170)/2=160/2=80 км/ч - скорость автомобиля, который двигался медленнее.

Answer 2

Problem Analysis

We are given that the distance between city A and city B is 360 km. Two cars simultaneously start from city A to city B. The speed of one car is 10 km/h greater than the speed of the other car. The car with the greater speed arrives at the destination 1/2 hour earlier than the other car. We need to find the speed of each car.

Solution

Let's assume the speed of the slower car is x km/h. Therefore, the speed of the faster car is x + 10 km/h.

We know that time = distance / speed.

The time taken by the slower car to travel the distance of 360 km is given by: time1 = 360 / x hours.

The time taken by the faster car to travel the same distance is given by: time2 = 360 / (x + 10) hours.

According to the problem, the faster car arrives at the destination 1/2 hour earlier than the slower car. Therefore, we can write the equation: time1 - time2 = 1/2 hours.

Substituting the values of time1 and time2, we get: (360 / x) - (360 / (x + 10)) = 1/2.

To solve this equation, we can multiply both sides by 2x(x + 10) to eliminate the fractions: 2 * (360(x + 10)) - 2 * 360x = x(x + 10).

Simplifying the equation: 720x + 7200 - 720x = x^2 + 10x.

Combining like terms: 7200 = x^2 + 10x.

Rearranging the equation: x^2 + 10x - 7200 = 0.

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

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

For our equation, a = 1, b = 10, and c = -7200.

Substituting the values into the quadratic formula: x = (-10 ± √(10^2 - 4 * 1 * -7200)) / (2 * 1).

Simplifying the equation: x = (-10 ± √(100 + 28800)) / 2.

Calculating the discriminant: x = (-10 ± √28900) / 2.

Taking the square root: x = (-10 ± 170) / 2.

Simplifying further: x = (-10 + 170) / 2 or x = (-10 - 170) / 2.

Calculating the values: x = 160 / 2 or x = -180 / 2.

Therefore, the speed of the slower car is 80 km/h and the speed of the faster car is 90 km/h.

Answer

The speed of the slower car is 80 km/h and the speed of the faster car is 90 km/h.