Question

два пешехода должны выйти навстречу друг к друг из двух пунктов,расстояние между которыми 20км.Если первый выйдет на полчаса раньше второго,то он встретит второго пешехода через 2.5 часа после своего выхода.Если второй выйдет на 1 час раньше первого то он встретит первого пешехода через 2 ч40 мин после своего выхода.какова скорость каждого пешехода?

Answer 1

Пусть скорость первого V1, второго V2.

1) Первый пешеход шел 2,5 часа и прошел2,5*V1, второй шел 2 часа (на полчаса меньше первого) и прошел 2*V2. Т.к. они встретились, то в сумме прошли 20 км, т.е 2,5*V1+2*V2=20

2) Второй пешеход шел (2+2/3) часа и прошел V2*(2+2/3), первый шел (1+2/3) часа (на час меньше) и прошел V1*(1+2/3). Опять они вместе прошли 20 км, т.е. V1*(1+2/3)+V2*(2+2/3)=20

Избавимся от дробнвх чисел в обеих уравнениях (умножим первое на 2, второе на 3)

Получим

5*V1+4*V2=40

5*V1+8*V2=60

Вычтем из второго равенства первое. Получим

4*V2=20

V2=5 км/час

V1=(20-5*2)/2.5=4 км/час

Ответ: Скорость первого пешехода 4 км/час, втотоого 5 км/час

Answer 2

Problem Analysis

We have two pedestrians who are walking towards each other from two different points, with a distance of 20 km between them. The first pedestrian starts half an hour earlier than the second pedestrian. We are given two scenarios:

1. If the first pedestrian meets the second pedestrian 2.5 hours after their own departure. 2. If the second pedestrian meets the first pedestrian 2 hours and 40 minutes after their own departure.

We need to find the speed of each pedestrian.

Solution

Let's assume the speed of the first pedestrian is x km/h and the speed of the second pedestrian is y km/h.

In the first scenario, the first pedestrian meets the second pedestrian 2.5 hours after their own departure. This means that the first pedestrian has been walking for 2.5 hours, while the second pedestrian has been walking for only 2 hours. Since the distance covered by both pedestrians is the same (20 km), we can set up the following equation:

Distance covered by the first pedestrian = Distance covered by the second pedestrian

Speed of the first pedestrian * Time taken by the first pedestrian = Speed of the second pedestrian * Time taken by the second pedestrian

Using the given information, we can substitute the values:

x * 2.5 = y * 2

In the second scenario, the second pedestrian meets the first pedestrian 2 hours and 40 minutes after their own departure. This means that the second pedestrian has been walking for 2 hours and 40 minutes, while the first pedestrian has been walking for only 2 hours. Again, since the distance covered by both pedestrians is the same (20 km), we can set up the following equation:

Distance covered by the first pedestrian = Distance covered by the second pedestrian

Speed of the first pedestrian * Time taken by the first pedestrian = Speed of the second pedestrian * Time taken by the second pedestrian

Converting 2 hours and 40 minutes to hours, we get 2.67 hours. Using the given information, we can substitute the values:

x * 2 = y * 2.67

Now we have a system of two equations with two variables:

1. x * 2.5 = y * 2 2. x * 2 = y * 2.67

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution. We can rearrange equation 1 to solve for x:

x = (y * 2) / 2.5

Substituting this value of x into equation 2, we get:

((y * 2) / 2.5) * 2 = y * 2.67

Simplifying the equation:

y * 1.6 = y * 2.67

Dividing both sides by y:

1.6 = 2.67

This equation is not true, which means there is no solution for this system of equations. It seems there might be an error in the given information or the problem setup.

Please double-check the given information and let me know if there are any corrections or additional details.