Question

Из пункта а в пункт б расстояние между которыми 34,вышел пешеход.Через полчаса на встречу ему из б в а выехал велосепедист.Велосепедист ехал со скоростью на 8 км/ч больше пешехода.Найдите скорость велосепедиста,если известно,что они встретились в 10 км от пункта а.

Answer 1

 x- скорость 1(v1);

x+8-скорость2(v2);

10/x - время1(t1);

(34-10)/(x+8) - время2(t2);

Осталось лишь из этого составить логическое уравнение:

t1=t2+полчаса

10/x=(34-10)/(x-8)+0,5

10/x=24/(x-8)+0,5

10/x=(48+x+8)/(2x+16)

10/x-(48+x+8)/(2x+16)=0

(20x+160-56x-x^2)/x(2x+16)=0

20x+160-56x-x^2=0

 

 x^2+36x-160=0

 

 D=1296+640=1936=44^2

x1=(-36+44)/2=8/2=4

x2=(-36-44)/2=-40 - не подходит, т.к. скорость в данном случае не может быть отрицательной.

v2=v1+8=4+8=12 км/ч

Ответ: скорость велосипедиста(v2)=12 км/ч.

 

Answer 2

Problem Analysis

We are given that the distance between point A and point B is 34 km. A pedestrian starts walking from point A to point B, and after half an hour, a cyclist starts cycling from point B to point A. The cyclist's speed is 8 km/h faster than the pedestrian's speed. We need to find the speed of the cyclist if they meet 10 km away from point A.

Solution

Let's assume the speed of the pedestrian is x km/h. Since the cyclist's speed is 8 km/h faster, the cyclist's speed is x + 8 km/h.

We know that the time taken by the pedestrian to cover a certain distance is equal to the time taken by the cyclist to cover the same distance. Let's calculate the time taken by each of them.

The time taken by the pedestrian to cover the distance between point A and the meeting point is 0.5 hours (since they started half an hour earlier).

The time taken by the cyclist to cover the distance between point B and the meeting point is t hours.

We can use the formula speed = distance / time to calculate the time taken by the cyclist.

The distance between the meeting point and point A is 10 km.

Using the formula speed = distance / time, we can write the equation:

x = 10 / 0.5 (for the pedestrian)

(x + 8) = 10 / t (for the cyclist)

Simplifying the second equation, we get:

x + 8 = 10 / t

Solving these two equations simultaneously will give us the value of x, which is the speed of the pedestrian, and t, which is the time taken by the cyclist.

Let's solve the equations:

x = 10 / 0.5

x + 8 = 10 / t

Calculation

Using the first equation:

x = 10 / 0.5

x = 20 km/h

Substituting the value of x in the second equation:

20 + 8 = 10 / t

28 = 10 / t

Cross-multiplying:

28t = 10

Dividing both sides by 28:

t = 10 / 28

t ≈ 0.357 hours

The time taken by the cyclist is approximately 0.357 hours.

Now, let's find the speed of the cyclist:

x + 8 = 20 + 8

x + 8 = 28 km/h

Therefore, the speed of the cyclist is 28 km/h.

Answer

The speed of the cyclist is 28 km/h.

Note: The calculations were done based on the given information and assumptions.