Question

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

Answer 1

X
x+20
60+32=92 км -весь пусть
92км/ч - средняя скорось
92/2-20= 26 км/ч- по шоссе
46+20=66км/ч - по автостраде

Answer 2

Calculation of Speed on the Highway and Road

To find the speed of the car on each segment of the journey, we can use the formula:

Speed = Distance / Time

Given that the car traveled 60 km on the highway and 32 km on the road, and the total time taken for the entire journey was 1 hour, we can calculate the speed on each segment.

Let's denote the speed on the highway as x km/h and the speed on the road as y km/h.

The time taken on the highway can be calculated as:

Time on Highway = Distance on Highway / Speed on Highway

Similarly, the time taken on the road can be calculated as:

Time on Road = Distance on Road / Speed on Road

Since the total time taken for the journey is 1 hour, we have:

Time on Highway + Time on Road = 1 hour

Now, let's substitute the given values and solve for the speeds on each segment.

Calculation

Given: - Distance on the highway = 60 km - Distance on the road = 32 km - Total time taken = 1 hour - Speed on the highway = Speed on the road + 20 km/h

Using the formulas mentioned above, we can set up the following equations:

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

Simplifying the equation:

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

Expanding and rearranging the equation:

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

92x - 1200 = x^2 - 20x

x^2 - 112x + 1200 = 0

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

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

For this equation, a = 1, b = -112, and c = 1200.

Solving the equation, we find two possible values for x: 12 and 100.

Since the speed on the road cannot be negative, we can discard the solution x = 12.

Therefore, the speed on the highway (x) is 100 km/h.

To find the speed on the road (y), we can substitute the value of x into the equation:

y = x - 20

y = 100 - 20

y = 80 km/h

Answer

The speed of the car on the highway is 100 km/h, and the speed on the road is 80 km/h.

Please note that these calculations are based on the given information and assumptions.