Question

Из пункта А в пункт Б расстояние между которыми 30 километров велосипедист ехал с определенной скоростью а вращался со скоростью на 3 кмч больше и потратил на 30 минут меньше чем на дорогу из а в б Найдите начальную скорость велосипедиста

Answer 1

Начальная скорость х км/ч, на обратном пути (х+3)км/ч, 30мин= 0,5ч
30/х-30/(х+3)=0,5
30х+90-30х=0,5х(х+3)
0,5х²+1,5х-90=0 /*2
х²+3х-180=0
D=9+4*180=729
x₁=(-3-27)/2=-15 (посторонний корень)
x₂=(-3+27)/2=12
Начальная скорость велосипедиста 12 км/ч

Answer 2

Calculation of the Initial Speed of the Cyclist

To find the initial speed of the cyclist, we can use the information provided in the question. Let's break down the problem step by step:

1. The distance between point A and point B is 30 kilometers. 2. The cyclist traveled at a certain speed from point A to point B. 3. The cyclist rotated at a speed that was 3 km/h faster than their traveling speed. 4. The cyclist took 30 minutes less time for the return journey from point B to point A compared to the journey from point A to point B.

Let's denote the cyclist's traveling speed as x km/h. According to the given information, the cyclist's rotation speed would be (x + 3) km/h.

Now, let's calculate the time it took for the cyclist to travel from point A to point B and from point B to point A.

The time taken to travel from A to B can be calculated using the formula:

Time = Distance / Speed

For the journey from A to B, the time taken is:

Time(A to B) = 30 km / x km/h

The time taken to travel from B to A would be:

Time(B to A) = 30 km / (x + 3) km/h

According to the question, the time taken for the return journey (B to A) is 30 minutes less than the time taken for the journey from A to B.

Converting 30 minutes to hours, we have:

30 minutes = 30 / 60 = 0.5 hours

So, we can write the equation:

Time(B to A) = Time(A to B) - 0.5 hours

Substituting the values, we get:

30 km / (x + 3) km/h = 30 km / x km/h - 0.5 hours

To solve this equation and find the value of x, we can cross-multiply and simplify:

30 km * x km/h = 30 km * (x + 3) km/h - 0.5 hours * x km/h * (x + 3) km/h

Simplifying further:

30x = 30(x + 3) - 0.5x(x + 3)

Expanding and rearranging the equation:

30x = 30x + 90 - 0.5x^2 - 1.5x

Combining like terms:

0 = -0.5x^2 - 1.5x + 90

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -0.5, b = -1.5, and c = 90.

Plugging in the values, we get:

x = (-(-1.5) ± √((-1.5)^2 - 4(-0.5)(90))) / (2(-0.5))

Simplifying further:

x = (1.5 ± √(2.25 + 180)) / (-1)

x = (1.5 ± √182.25) / (-1)

Taking the square root:

x = (1.5 ± 13.5) / (-1)

We have two possible solutions:

1. x = (1.5 + 13.5) / (-1) = 15 / (-1) = -15 2. x = (1.5 - 13.5) / (-1) = -12 / (-1) = 12

Since speed cannot be negative, we can discard the solution x = -15.

Therefore, the initial speed of the cyclist is 12 km/h.

Please note that the calculations provided above are based on the information given in the question.