Question

7 марта 2018 года по единственной дороге, соединяющей города А и Б, ехали с постоянными скоростями два автомобиля. Первый выехал из города А в 07:00 и прибыл в город Б в 20:00 этого же дня, а второй выехал из города Б в 08:00 и прибыл в А в 21:00 этого же дня. В какое время они встретились?

Answer 1

С 7:00 до 20:00 столько же времени, как с 8:00 до 21:00. 13 часов.
Значит, они ехали с одинаковыми скоростями.
Пусть будет 50 км/ч. Тогда расстояние АВ=50*13=650 км.
Видимо, это были Москва и Санкт-Петербург. Между ними ровно 650.
С 7:00 до встречи в t ч 1 машина прошла x км, а 2 с 8:00 до t ч 650-x км.
x = (t-7)*50
650-x = (t-8)*50
Подставляем 1 уравнение во 2 уравнение.
650-(t-7)*50 = (t-8)*50
Делим все на 50
13-(t-7) = t-8
13 = 2t-15
2t = 13+15 = 28
t = 14
Они встретились в 14:00.

Answer 2

Answer in detail. On March 7, 2018, two cars were driving along the only road connecting cities A and B at constant speeds. The first one left city A at 07:00 and arrived in city B at 20:00 on the same day, and the second one left city B at 08:00 and arrived in A at 21:00 on the same day. At what time did they meet?

To answer this question, we need to find the distance between the two cities and the speeds of the two cars. Then we can use the formula for the time of meeting:

$$t = \frac{d}{v_1 + v_2}$$

where $t$ is the time of meeting in hours, $d$ is the distance between the cities in kilometers, and $v_1$ and $v_2$ are the speeds of the cars in kilometers per hour.

We can find the distance between the cities by using the information given in the question. The first car traveled from A to B in 13 hours, so the distance is:

$$d = v_1 \times 13$$

The second car traveled from B to A in 13 hours, so the distance is also:

$$d = v_2 \times 13$$

Since the distance is the same, we can equate the two expressions and solve for $v_1$:

$$v_1 \times 13 = v_2 \times 13$$

$$v_1 = v_2$$

This means that the two cars have the same speed. Let's call it $v$. Then the distance between the cities is:

$$d = v \times 13$$

Now we can use the formula for the time of meeting and substitute the values:

$$t = \frac{d}{v_1 + v_2}$$

$$t = \frac{v \times 13}{v + v}$$

$$t = \frac{13}{2}$$

$$t = 6.5$$

This means that the two cars met after 6.5 hours from the time the first car left city A. Since the first car left at 07:00, the time of meeting is:

$$07:00 + 6.5 = 13:30$$

Therefore, the two cars met at 13:30 on March 7, 2018.