Question

Из пунктов A и B, расстояние между которыми 27 км, вышли одновременно навстречу друг другу два пешехода и встретились в 15 км от А. Найдите скорость пешехода, шедшего из А, если известно, что он шёл со скоростью, на 2 км/ч большей, чем второй пешеход, и сделал в пути получасовую остановку. (подробное решение)

Answer 1

Пусть х - скорость первого пешехода в км/ч.
Тогда x-2 - скорость 2-го пешехода
$\frac{15}{x} + \frac{1}{2}$ - время, затраченное первым до встречи в часах..
Т.к. второй пешеход до встречи прошел 27-15=12 км., то
$\frac{12}{x-2}$ - время, затраченное вторым до встречи.
Поскольку вышли одновременно и встретились, затратили одинаковое время, то есть верно уравнение
$\frac{15}{x} + \frac{1}{2} = \frac{12}{x-2}$
Переносим все в левую часть и приводим к общему знаменателю:
$\frac{15\cdot 2(x-2) +x(x-2)-12\cdot 2x}{2x(x-2)}=0$
Раскрываем скобки и упрощаем числитель, получаем
$15\cdot 2(x-2) +x(x-2)-12\cdot 2x=x^2+4x-60=0$
Решаем его, получаем x=6 и -10. Отрицательный ответ не подходит, поэтому ответ x=6 км/ч.

Answer 2

Problem Analysis

We have two pedestrians walking towards each other from points A and B, which are 27 km apart. They meet 15 km from point A. We need to find the speed of the pedestrian walking from point A, given that they walked at a speed 2 km/h faster than the other pedestrian and took a 30-minute break during the journey.

Solution

Let's assume the speed of the pedestrian walking from point A is v km/h. The speed of the other pedestrian will be v - 2 km/h.

We can calculate the time it took for the pedestrians to meet by dividing the distance they covered by their respective speeds. The pedestrian from point A covered a distance of 15 km, and the other pedestrian covered a distance of 27 - 15 = 12 km.

The time taken by the pedestrian from point A is given by: time = distance / speed = 15 / v hours.

The time taken by the other pedestrian is given by: time = distance / speed = 12 / (v - 2) hours.

Since they started at the same time, these two times are equal. We can set up the following equation:

15 / v = 12 / (v - 2).

To solve this equation, we can cross-multiply and simplify:

15(v - 2) = 12v.

Expanding and rearranging the equation, we get:

15v - 30 = 12v.

Simplifying further, we have:

3v = 30.

Dividing both sides by 3, we find:

v = 10.

Therefore, the speed of the pedestrian walking from point A is 10 km/h.

Answer

The speed of the pedestrian walking from point A is 10 km/h.

Explanation

The pedestrian walking from point A covered a distance of 15 km. The other pedestrian covered a distance of 12 km. Since they walked at different speeds, the pedestrian from point A took less time to cover the same distance. This is because the pedestrian from point A walked at a speed 2 km/h faster than the other pedestrian. Additionally, the pedestrian from point A took a 30-minute break during the journey.

By solving the equation, we found that the speed of the pedestrian walking from point A is 10 km/h.