Question

Из Москвы в Киев вышел поезд со скоростью 80 километров час спустя 24 минуты из Киева в Москву отправился поезд скорость которого равна 70 километров час через сколько часов после выхода поезда из Киева произойдет встреча если расстояние от Москвы до Киева 872 километра?

Answer 1

24мин=0,4часа
80*0,4=32км прошел поезд из Москвы до выхода поезда из Киева
872-32=840км расстояние между поездами во время выхода поезда из Киева
80+70=150км/час скорость сближения
840:150=5,6 часа=5час.36мин. встретятся

Answer 2

Answer in detail. A train left Moscow for Kiev at a speed of 80 kilometers per hour, 24 minutes later a train left Kiev for Moscow at a speed of 70 kilometers per hour. How many hours after the departure of the train from Kiev will the meeting take place if the distance from Moscow to Kiev is 872 kilometers?

To solve this problem, we need to find the time when the two trains will have traveled a total distance of 872 kilometers. We can use the formula:

$$d = vt$$

where $d$ is the distance, $v$ is the speed, and $t$ is the time.

Let $t_1$ be the time when the train from Moscow left, and $t_2$ be the time when the train from Kiev left. Then, the distance traveled by the train from Moscow is:

$$d_1 = 80(t_2 - t_1)$$

and the distance traveled by the train from Kiev is:

$$d_2 = 70t_2$$

The total distance is:

$$d_1 + d_2 = 80(t_2 - t_1) + 70t_2 = 872$$

We are given that $t_2 - t_1 = 24/60 = 0.4$ hours. Substituting this into the equation, we get:

$$80(0.4) + 70t_2 = 872$$

Solving for $t_2$, we get:

$$t_2 = \frac{872 - 80(0.4)}{70} = 11.2$$

Therefore, the meeting will take place 11.2 hours after the departure of the train from Kiev.