Question

расстояние между городами А и Б равно 1060 км. из города А отправился поезд со скоростью 40 км / ч,а через 4 ч навстречу ему отправился поезд из города Б со скоростью 50 км/ч. Через сколько часов после отправления второго поезда и на каком расстояние от города А встретятся эти поезда?

Answer 1

Problem Analysis

We are given that the distance between cities A and B is 1060 km. A train departs from city A with a speed of 40 km/h, and after 4 hours, another train departs from city B towards city A with a speed of 50 km/h. We need to determine how many hours after the departure of the second train the two trains will meet, and at what distance from city A this meeting will occur.

Solution

Let's calculate the time it takes for the first train to meet the second train. We can use the formula:

Time = Distance / Speed

The distance covered by the first train in 4 hours is:

Distance = Speed * Time = 40 km/h * 4 h = 160 km

So, after 4 hours, the first train has covered a distance of 160 km.

Now, let's calculate the remaining distance between the two trains:

Remaining Distance = Total Distance - Distance Covered by First Train = 1060 km - 160 km = 900 km

The relative speed of the two trains is the sum of their speeds:

Relative Speed = Speed of First Train + Speed of Second Train = 40 km/h + 50 km/h = 90 km/h

Now, we can calculate the time it takes for the two trains to meet:

Time = Distance / Relative Speed = 900 km / 90 km/h = 10 hours

Therefore, the two trains will meet 10 hours after the departure of the second train.

To find the distance from city A where the meeting occurs, we can use the formula:

Distance = Speed * Time = 50 km/h * 10 h = 500 km

Therefore, the two trains will meet at a distance of 500 km from city A.

Answer

The two trains will meet 10 hours after the departure of the second train, and they will meet at a distance of 500 km from city A.