Question

Два автомобиля выежают одновременно из одного города в другой,находяшийся на растоянии 560 км.Скорость первого на 10км/ч больше скорости второго,и поэтому первый автомобиль приежает на место на 1 раньше второго.Определите скорость каждого автомобиля.

Answer 1

Если скорость второго автомобиля х, скорость первого х+10.
Время, потраченное на дорогу вторым автомобилем, 560:х, первым - 560:(Х+10)
Второй ехал на 1 час дольше.
560:х-560:(х+10)=1
560х+5600- 560х =х²+10х
х²+10х-5600=0
Дискриминант равен:
D=b²-4ac=10²- 4·1·-5600=22500
x1=(-b+√D):2а=70
x2=-80; Его отбрасываем.
Скорость второго автомобиля 70км/час,
скорость первого автомобиля 80км/час.

Answer 2

Problem Analysis

We are given that two cars start simultaneously from one city to another city, which is 560 km away. The first car's speed is 10 km/h faster than the second car's speed. As a result, the first car arrives at the destination 1 hour earlier than the second car. We need to determine the speed of each car.

Solution

Let's assume the speed of the second car is x km/h. Then the speed of the first car would be x + 10 km/h.

We can use the formula distance = speed × time to solve this problem.

The time taken by the second car to travel 560 km is given by 560 / x hours.

The time taken by the first car to travel 560 km is given by 560 / (x + 10) hours.

According to the problem, the first car arrives at the destination 1 hour earlier than the second car. So, we can set up the following equation:

560 / x - 560 / (x + 10) = 1

Now, let's solve this equation to find the values of x and x + 10.

Calculation

To solve the equation, we can follow these steps:

1. Multiply both sides of the equation by x(x + 10) to eliminate the denominators. 2. Simplify the equation. 3. Rearrange the equation to get a quadratic equation in terms of x. 4. Solve the quadratic equation to find the values of x. 5. Calculate x + 10 to find the speed of the first car.

Let's perform the calculations step by step:

1. Multiply both sides of the equation by x(x + 10): 560(x + 10) - 560x = x(x + 10)

2. Simplify the equation: 560x + 5600 - 560x = x^2 + 10x

3. Rearrange the equation: x^2 + 10x - 5600 = 0

4. Solve the quadratic equation: Using the quadratic formula, we get: x = (-10 ± √(10^2 - 4 * 1 * (-5600))) / (2 * 1)

Simplifying further: x = (-10 ± √(100 + 22400)) / 2 x = (-10 ± √22500) / 2 x = (-10 ± 150) / 2

We have two possible solutions: - x = (-10 + 150) / 2 = 140 / 2 = 70 - x = (-10 - 150) / 2 = -160 / 2 = -80

5. Calculate x + 10 to find the speed of the first car: - For x = 70, the speed of the first car is 70 + 10 = 80 km/h. - For x = -80, the speed of the first car is -80 + 10 = -70 km/h.

Answer

Therefore, the speed of the first car is 80 km/h and the speed of the second car is 70 km/h.