Question

Из а в б вышел пешеход. Одновременно с ним из пункта б во встречном направлении выехал велосипедист. Они двигались с постоянными скоростями, и через час расстояние между ними равнялось 3 км, а ещё через час -14 км. Найдите расстояние между а и б.

Answer 1

Ответ А) 8 или 20 км

Answer 2

Problem Analysis

We have two individuals, a pedestrian and a cyclist, who start from points A and B, respectively. They move towards each other with constant speeds. After one hour, the distance between them is 3 km, and after another hour, the distance between them is 14 km. We need to find the distance between points A and B.

Solution

Let's assume the speed of the pedestrian is v km/h and the speed of the cyclist is u km/h.

After the first hour, the pedestrian has covered a distance of v km, and the cyclist has covered a distance of u km. The total distance between them is 3 km. Therefore, we can write the equation:

v + u = 3 After the second hour, the pedestrian has covered a distance of 2v km, and the cyclist has covered a distance of 2u km. The total distance between them is 14 km. Therefore, we can write the equation:

2v + 2u = 14 Now we have a system of two equations with two unknowns. We can solve this system to find the values of v and u.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation we can express v in terms of u:

v = 3 - u

Substituting this value of v into equation we get:

2(3 - u) + 2u = 14

Simplifying the equation:

6 - 2u + 2u = 14

The u terms cancel out, and we are left with:

6 = 14

This equation is not possible to solve because it is contradictory. It means that there is no solution that satisfies both equations simultaneously.

Conclusion

Based on the given information, there seems to be an error or inconsistency in the problem statement. The system of equations does not have a solution, which means that the given distances and times are not consistent with each other. Therefore, we cannot determine the distance between points A and B with the given information.

If you have any additional information or clarification regarding the problem, please provide it, and I'll be happy to assist you further.