Question

Товарный поезд идет со скоростью 10 м/с. Спустя 30 мин. с той же станции по тому же направлению вышел экспресс со скоростью 20 м/с. Через какое время после выхода товарного поезда и на каком расстоянии от станции экспресс догонит товарный поезд.

Answer 1

Извини за кривой почерк

Answer 2

Это решения исходя из графического способа. Ну тк и аналитически сойдёт 

Answer 3

Problem Analysis

We are given that a freight train is traveling at a speed of 10 m/s. After 30 minutes, an express train leaves the same station in the same direction at a speed of 20 m/s. We need to determine how long it will take for the express train to catch up to the freight train and at what distance from the station this will occur.

Solution

To solve this problem, we can use the formula:

Distance = Speed × Time

Let's denote the time it takes for the express train to catch up to the freight train as t and the distance from the station where they meet as d.

From the given information, we know that the freight train has been traveling for 30 minutes longer than the express train. Therefore, the time it has been traveling is t + 30 minutes.

Using the formula for distance, we can write the following equations:

For the freight train: Distance = Speed × Time d = 10 × (t + 30)

For the express train: Distance = Speed × Time d = 20 × t

Now we can solve these equations to find the values of t and d.

Calculation

Let's solve the equations:

From the equation for the freight train: d = 10 × (t + 30)

From the equation for the express train: d = 20 × t

Setting these two equations equal to each other, we have: 10 × (t + 30) = 20 × t

Simplifying the equation: 10t + 300 = 20t

Subtracting 10t from both sides: 300 = 10t

Dividing both sides by 10: t = 30

Now that we have the value of t, we can substitute it back into either of the equations to find the value of d.

Using the equation for the express train: d = 20 × t d = 20 × 30 d = 600

Therefore, the express train will catch up to the freight train after 30 minutes and at a distance of 600 meters from the station.

Answer

The express train will catch up to the freight train after 30 minutes and at a distance of 600 meters from the station.