Question

Автомобиль проехал 60км по автостраде и 32км по шоссе,затратив на весь путь 1ч.Найдите скорость автомобиля на каждом участке пути,если по автостраде он двигался на 20км/ч быстрее,чем по шоссе

Answer 1

всего он проехал 60+32=92 км

на первом участке ехал со скоростью х,на втором х+20,сост уравнение

х+20+х=92

2х=72

х=36

36+20=56

Ответ:на автостраде 56,на шоссе 36

Answer 2

Problem Analysis

We are given that a car traveled 60 km on a highway and 32 km on a road, taking a total of 1 hour. The car traveled 20 km/h faster on the highway compared to the road. We need to find the speed of the car on each segment of the journey.

Solution

Let's assume the speed of the car on the road is x km/h. Since the car traveled 20 km/h faster on the highway, the speed on the highway would be x + 20 km/h.

We can use the formula distance = speed × time to find the time taken on each segment.

On the highway: - Distance = 60 km - Speed = x + 20 km/h - Time = Distance / Speed = 60 / (x + 20) hours

On the road: - Distance = 32 km - Speed = x km/h - Time = Distance / Speed = 32 / x hours

The total time taken for the entire journey is given as 1 hour. Therefore, the sum of the times taken on each segment should be equal to 1 hour:

60 / (x + 20) + 32 / x = 1

To solve this equation, we can multiply through by x(x + 20) to eliminate the denominators:

60x + 1200 + 32(x + 20) = x(x + 20)

Simplifying the equation:

60x + 1200 + 32x + 640 = x^2 + 20x

92x + 1840 = x^2 + 20x

Rearranging the equation:

x^2 - 72x - 1840 = 0

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

Calculation

Using the quadratic formula, we have:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -72, and c = -1840.

Plugging in the values:

x = (-(-72) ± √((-72)^2 - 4(1)(-1840))) / (2(1))

Simplifying:

x = (72 ± √(5184 + 7360)) / 2

x = (72 ± √12544) / 2

x = (72 ± 112) / 2

We have two possible solutions:

1. x = (72 + 112) / 2 = 92 km/h 2. x = (72 - 112) / 2 = -20 km/h (negative speed is not possible in this context)

Therefore, the speed of the car on the road is 92 km/h and on the highway is 92 + 20 = 112 km/h.

Answer

The speed of the car on the road is 92 km/h and on the highway is 112 km/h.