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

Пусть x (км/ч) - скорость по шоссе, тогда по автостраде - (x+20)  км/ч.

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

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

60x+32x+640=x*x+20x

x*x+20x-60x-32x-640=0

x*x-72x-640=0

D=5184+2560=7744=88*88

x=(72+88)/2=80 (км/ч) - скорость по шоссе

80+20=100 (км/ч) - скорость по автостраде

Ответ: 80км/ч, 100км/ч

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. We need to find the speed of the car on each segment of the journey, given that the car traveled 20 km/h faster on the highway compared to the road.

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.

To find the time taken on each segment, we can use the formula time = distance / speed.

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

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

According to the problem, the total time taken for the entire journey is 1 hour. Therefore, the sum of the times taken on each segment should be equal to 1 hour.

We can set up the following equation to solve for x:

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

Let's solve this equation to find the value of x.

Calculation

To solve the equation, we can multiply both sides 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

Combining like terms:

92x + 1840 = x^2 + 20x

Rearranging the equation:

x^2 + 20x - 92x - 1840 = 0

x^2 - 72x - 1840 = 0

Now we can solve this quadratic equation.