Question

Пассажирский поезд проходит расстояние между двумя городами за 10 ч, а товарный – за 15 ч. Оба поезда вышли одновременно из городов навстречу друг другу. Через сколько часов они встретятся? Дайте ответ в часах.

Answer 1

х-расстояние между городами

х/15 -скорость товарняка

х/10-скорость пассажирского

х/15+х/10-скорость сближения поездов

значит поезда встретятся через

$\frac{x}{\frac{x}{15}+\frac{x}{10}}=\frac{x}{\frac{10x+15x}{150}}=\frac{150x}{25x}=6$

ответ поезда встретятся через 6 часов

Answer 2

Встретятся через 6 часов

 

Answer 3

Problem Analysis

We are given that a passenger train covers a distance between two cities in 10 hours, while a freight train covers the same distance in 15 hours. Both trains start from their respective cities simultaneously and move towards each other. We need to determine how many hours it will take for them to meet.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed of two objects moving towards each other is the sum of their individual speeds. Let's assume the speed of the passenger train is vA and the speed of the freight train is vB.

The relative speed of the two trains is given by the equation: relative speed = vA + vB.

We know that the passenger train covers the distance between the two cities in 10 hours, and the freight train covers the same distance in 15 hours. Let's assume the distance between the two cities is d.

Using the formula distance = speed × time, we can write the following equations: d = vA × 10 (equation 1) d = vB × 15 (equation 2)

We can solve these two equations simultaneously to find the values of vA and vB.

Once we have the values of vA and vB, we can find the time it takes for the two trains to meet by dividing the distance between the two cities by their relative speed: time = d / (vA + vB).

Let's calculate the time it takes for the two trains to meet.

Calculation

From equation 1, we have: d = vA × 10.

From equation 2, we have: d = vB × 15.

Equating the two equations, we get: vA × 10 = vB × 15.

Simplifying the equation, we have: vA = (vB × 15) / 10.

Substituting this value of vA in equation 1, we get: d = ((vB × 15) / 10) × 10.

Simplifying further, we have: d = vB × 15.

Now, we can substitute the value of d in the equation for time: time = d / (vA + vB) = (vB × 15) / ((vB × 15) / 10 + vB).

Simplifying the equation, we have: time = (vB × 15) / ((vB × 15 + 10vB) / 10) = (vB × 15 × 10) / (vB × 15 + 10vB).

Simplifying further, we have: time = (vB × 150) / (vB × 15 + 10vB) = (vB × 150) / (25vB) = 150 / 25 = 6.

Therefore, the two trains will meet after 6 hours.

Answer

The passenger train and the freight train will meet after 6 hours.

Explanation

The passenger train and the freight train have different speeds. The passenger train covers the distance between the two cities in 10 hours, while the freight train covers the same distance in 15 hours. Since the two trains are moving towards each other, their relative speed is the sum of their individual speeds. By calculating the relative speed and dividing the distance between the two cities by the relative speed, we find that the two trains will meet after 6 hours.