Question

Два автомоббиля отпровляются в 420 километровый пробег первый едет со скорость на 10 км больше второго и прибывает к финишу на час раньше второго. найдите скорость автомобиля пришедшего к финишу вторым

Answer 1

420:2=210:10=21......

Answer 2

Problem Analysis

We are given two cars that are traveling a distance of 420 kilometers. The first car is traveling at a speed that is 10 km/h faster than the second car. The first car arrives at the finish line one hour earlier than the second car. We need to find the speed of the second car.

Solution

Let's assume the speed of the second car is x km/h. Since the first car is traveling 10 km/h faster, its speed would be x + 10 km/h.

We can use the formula speed = distance / time to calculate the time taken by each car to complete the 420-kilometer distance.

For the first car: - Speed = x + 10 km/h - Distance = 420 km - Time = Distance / Speed = 420 / (x + 10) hours

For the second car: - Speed = x km/h - Distance = 420 km - Time = Distance / Speed = 420 / x hours

According to the problem, the first car arrives at the finish line one hour earlier than the second car. So, we can set up the following equation:

Time taken by the second car - Time taken by the first car = 1 hour

(420 / x) - (420 / (x + 10)) = 1

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation (420 / x) - (420 / (x + 10)) = 1, we can multiply both sides of the equation by x(x + 10) to eliminate the denominators.

(x(x + 10)) * (420 / x) - (x(x + 10)) * (420 / (x + 10)) = 1 * (x(x + 10))

420(x + 10) - 420x = x(x + 10)

420x + 4200 - 420x = x^2 + 10x

4200 = x^2 + 10x

x^2 + 10x - 4200 = 0

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

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

In this case, a = 1, b = 10, and c = -4200.

x = (-10 ± √(10^2 - 4 * 1 * -4200)) / (2 * 1)

x = (-10 ± √(100 + 16800)) / 2

x = (-10 ± √16900) / 2

x = (-10 ± 130) / 2

x = (120 / 2) or (-140 / 2)

x = 60 or -70

Since speed cannot be negative, the speed of the second car is 60 km/h.

Answer

The speed of the car that arrived at the finish line second is 60 km/h.