Question

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

Answer 1

Ответ: 8 или 20 км. Решение: Пусть расстояние между А и В равно х. Тогда через час они вдвоем преодолели расстояние х-3 или х+3, а за два часа  х+14. Рассмотрим оба случая. Первый: 2х-6=х+14, х=20. Второй: 2х+6=х+14, х=8.

Answer 2

Calculating the Distance Between Points A and B

To find the distance between points A and B, we can use the information provided about the pedestrian and the cyclist moving with constant speeds.

Let's denote: - The speed of the pedestrian as v (in km/h) - The speed of the cyclist as u (in km/h) - The initial distance between A and B as d (in km)

After 1 hour, the distance between them is 3 km, and after another hour, the distance becomes 14 km.

Using this information, we can set up the following equations:

1. After 1 hour: - d + v = 3 2. After 2 hours: - d + 2v + u = 14 We can solve these equations to find the values of v and u.

Solving the Equations

Subtracting the first equation from the second equation, we get: - 2v + u = 11

Now, we can use this information to solve for the values of v and u.

Finding the Values of v and u

Given the equations: - d + v = 3 - 2v + u = 11

We can solve for v and u by substituting the value of d from the first equation into the second equation.

After solving for v and u, we can use these values to find the initial distance d between points A and B.

Let's proceed with the calculations.