Question

Из города в деревню вышел викентий ,а навстречу ему из деревни в город одновременно вышел афанасий. найти расстояние между деревней и городом,если известно ,что расстояние между пешеходами равнялась2 км дважды: сначало ,когда викентий прошел половину пути до деревни и потом ,когда афанасий прошел треть пути до города

Answer 1

В -скорость Викентия, А -Афанасия, путь С.
С/2В -время до первого раза
С*А/2В -расстояние пройденное Афанасием к времени первого раза.
С/2-С*А/2В =2
С/3А- время до второго раза
С*В/3А -прошел Викентий до второго раза.
С*В/3А-2С/3=2
Обозначим   А/В=х
1/2-х/2=2/С
 1/3х-2/3=2/С
1/2-х/2=1/3х-2/3
3х/2-3х*х/2=1-2х
3х-3х*х=2-4х
х-х*х=2/3-4х/3
х*х-7х/3+2/3=0
(х-7/6)*(х-7/6)=25/36
х-7/6=5/6 или х-7/6=-5/6
Викентий идет быстрее Афанасия значит х=1/3
подставляем х:
С/2-С/6=2
3С-С=12
2С=12
С=6 км
Ответ: 6 км

Answer 2

Problem Analysis

We are given that Vikentiy walked from the city to the village, while Afanasiy walked from the village to the city. The distance between the two pedestrians was 2 km when Vikentiy had covered half the distance to the village, and it was 2 km again when Afanasiy had covered one-third of the distance to the city. We need to find the distance between the village and the city.

Solution

Let's assume the distance between the village and the city is x km.

According to the problem, when Vikentiy had covered half the distance to the village, the distance between the two pedestrians was 2 km. This means that Vikentiy had covered x/2 km at that point.

Similarly, when Afanasiy had covered one-third of the distance to the city, the distance between the two pedestrians was again 2 km. This means that Afanasiy had covered (2/3)x km at that point.

To find the distance between the village and the city, we need to solve the equation:

x/2 + (2/3)x = 2

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

Equation Solution

To solve the equation, we can multiply both sides by 6 to eliminate the denominators:

3x + 4x = 12

Simplifying the equation:

7x = 12

Dividing both sides by 7:

x = 12/7

Therefore, the distance between the village and the city is 12/7 km.

Answer

The distance between the village and the city is 12/7 km.

Answer 3

Problem Analysis

We are given that Vikentiy walked from the city to the village, while Afanasiy walked from the village to the city. We need to find the distance between the village and the city, given that the distance between the two pedestrians was 2 km at two different points in time: when Vikentiy had walked half the distance to the village, and when Afanasiy had walked one-third of the distance to the city.

Solution

Let's assume the distance between the village and the city is x km.

According to the problem, when Vikentiy had walked half the distance to the village, the distance between the two pedestrians was 2 km. This means that Vikentiy had walked x/2 km at that point.

Similarly, when Afanasiy had walked one-third of the distance to the city, the distance between the two pedestrians was again 2 km. This means that Afanasiy had walked (2/3)x km at that point.

To find the distance between the village and the city, we need to solve the equation:

(x/2) + (2/3)x = 2

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

Equation Solving

To solve the equation, we can simplify it by multiplying through by 6 to eliminate the fractions:

3x + 4x = 12

7x = 12

x = 12/7

So, the distance between the village and the city is 12/7 km.

Answer

The distance between the village and the city is 12/7 km.

Explanation

When Vikentiy had walked half the distance to the village, the distance between the two pedestrians was 2 km. This implies that Vikentiy had walked 6/7 km at that point. Similarly, when Afanasiy had walked one-third of the distance to the city, the distance between the two pedestrians was again 2 km. This implies that Afanasiy had walked 8/7 km at that point. Therefore, the total distance between the village and the city is 6/7 km + 8/7 km = 14/7 km = 2 km.