Question

ПОМОГИТЕ ПОЖАЛУЙСТА,СРОЧНО!!!! Велосипедист проехал 20 км по дороге ведущей в гору,и 60 км по ровной местности,затратив на весь путь 6 ч.С какой скоростью ехал велосипедист на каждом участке пути,если известно,что в гору он ехал со скоростью,на 5 км/ч меньше,чем по ровной местности?

Answer 1

пусть х скорость на ровной дороге

20/(х-5)+60/х=6

20х+60х-300-6х^2+30х=0

3х^2-55х+150=0

дискриминант 35

х=(55+35)/6=15

х=15 км/ч это на ровной дороге

15-5=10 км/ч на дороге, ведущей в гору

Answer 2

Problem Analysis

We are given that a cyclist traveled 20 km uphill and 60 km on flat ground, taking a total of 6 hours for the entire journey. We need to determine the speed at which the cyclist traveled on each segment of the route, knowing that the speed uphill was 5 km/h slower than on flat ground.

Solution

Let's assume the speed of the cyclist on flat ground is x km/h. According to the given information, the speed uphill is 5 km/h slower, so the speed uphill is (x - 5) km/h.

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

The time taken for the uphill segment is 20 km / (x - 5) km/h.

The time taken for the flat ground segment is 60 km / x km/h.

Since the total time for the entire journey is 6 hours, we can write the equation: (20 / (x - 5)) + (60 / x) = 6.

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

Calculation

To solve the equation, we can multiply through by x(x - 5) to eliminate the denominators:

(20x) + (60(x - 5)) = 6x(x - 5).

Expanding and simplifying the equation:

20x + 60x - 300 = 6x^2 - 30x.

Rearranging the equation to form a quadratic equation:

6x^2 - 30x - 20x - 60x + 300 = 0.

Combining like terms:

6x^2 - 110x + 300 = 0.

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

Using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = 6, b = -110, and c = 300.

Calculating the discriminant: b^2 - 4ac = (-110)^2 - 4(6)(300) = 12100 - 7200 = 4900.

Since the discriminant is positive, we have two real solutions.

Calculating the solutions:

x = (-(-110) ± sqrt(4900)) / (2(6)).

Simplifying:

x = (110 ± 70) / 12.

Calculating the two possible values of x:

x1 = (110 + 70) / 12 = 180 / 12 = 15.

x2 = (110 - 70) / 12 = 40 / 12 = 10/3 ≈ 3.33.

Since the speed of the cyclist cannot be negative, we discard the negative solution.

Therefore, the speed of the cyclist on flat ground is approximately 15 km/h.

The speed of the cyclist uphill is 5 km/h slower, so the speed uphill is approximately 10 km/h.

Answer

The cyclist traveled at a speed of approximately 15 km/h on flat ground and approximately 10 km/h uphill.

Note: The above calculations are based on the given information and assumptions.