Question

Помогите решить задачу в 22ч00мин от перрона ленинградского вокзала Москвы в сторону Санкт-Петербурга отошёл пассажирский поезд, средняя скорость которого 72км\ч. в 23ч10мин с того же вокзала в том же направлении отправился скорый поезд со средней скоростью 84км\ч. какое расстояние будет между поездами в 00ч 05 мин?

Answer 1

00ч 05мин.-22ч 00мин=2ч 05мин ехал пассажирский поезд
$72*2\frac{5}{60}=72*2 \frac{1}{12}=72* \frac{25}{12}=150$ км. проехал пассажирский поезд
00ч. 05мин.-23ч. 10мин.=55 мин. проехал скорый поезд
$84* \frac{55}{60}=84* \frac{11}{12}=77$ км проехал скорый поезд
150-77=73 км. будет расстояние между поездами.

Answer 2

To find the distance between the two trains at a specific time, we need to calculate the distance each train has traveled from the starting point.

Let's break down the problem step by step:

1. The passenger train departs from Leningradsky Station in Moscow towards St. Petersburg at 22:00. Its average speed is 72 km/h. 2. The express train departs from the same station in the same direction at 23:10. Its average speed is 84 km/h. 3. We need to find the distance between the two trains at 00:05.

To solve this problem, we can calculate the distance each train has traveled by multiplying its speed by the time it has been traveling.

Distance traveled by the passenger train:

The passenger train departs at 22:00 and travels for 2 hours and 5 minutes (from 22:00 to 00:05).

To convert 2 hours and 5 minutes to hours, we can add the minutes to the hours: 2 hours + 5 minutes / 60 minutes = 2.0833 hours.

The distance traveled by the passenger train can be calculated as follows: Distance = Speed * Time Distance = 72 km/h * 2.0833 hours

Distance traveled by the express train:

The express train departs at 23:10 and travels for 55 minutes (from 23:10 to 00:05).

To convert 55 minutes to hours, we divide it by 60: 55 minutes / 60 minutes = 0.9167 hours.

The distance traveled by the express train can be calculated as follows: Distance = Speed * Time Distance = 84 km/h * 0.9167 hours

Now, let's calculate the distances:

Distance traveled by the passenger train = 72 km/h * 2.0833 hours = 149.99 km (approximately 150 km) [[1]] Distance traveled by the express train = 84 km/h * 0.9167 hours = 77.17 km (approximately 77 km) [[2]]

To find the distance between the two trains at 00:05, we subtract the distance traveled by the express train from the distance traveled by the passenger train:

Distance between the two trains = Distance traveled by the passenger train - Distance traveled by the express train Distance between the two trains = 150 km - 77 km = 73 km

Therefore, at 00:05, the distance between the passenger train and the express train will be approximately 73 kilometers.