Question

Из городов а и в, расстояние между которыми 180 км, отправлены в одно и тоже время два поезда навстречу друг другу. После их встречи поезд, вышедший из А, прибывает в В через 2 часа, а другой прибывает в А через 4 часа 30 минут. найдите скорость каждого поезда

Answer 1

180:2=90 км.ч скорость поезда АВ
180:4.5=40км.ч скорость поезда ВА

Answer 2

Problem Analysis

We are given that two trains start from cities A and B, which are 180 km apart, and travel towards each other. After their meeting, the train that started from A arrives at B in 2 hours, while the other train arrives at A in 4 hours and 30 minutes. We need to find the speed of each train.

Solution

Let's assume the speed of the train starting from A is vA and the speed of the train starting from B is vB.

To find the speed of each train, we can use the formula:

Speed = Distance / Time

We know that the distance between the two cities is 180 km.

Let's calculate the time taken by each train to meet:

The train starting from A takes 2 hours to reach B after the meeting. So, the total time taken by this train is the time taken to meet + the time taken to travel from the meeting point to B. Let's call the time taken to meet as t.

The train starting from B takes 4 hours and 30 minutes to reach A after the meeting. So, the total time taken by this train is the time taken to meet + the time taken to travel from the meeting point to A. Let's call the time taken to meet as t.

Now, we can write the equations:

Distance = Speed * Time

For the train starting from A: 180 km = vA * (t + 2)

For the train starting from B: 180 km = vB * (t + 4.5)

We have two equations and two unknowns (vA and vB). We can solve these equations to find the values of vA and vB.

Let's solve the equations:

180 = vA * (t + 2) --(1)

180 = vB * (t + 4.5) --(2)

From equation (1), we can express t in terms of vA:

t = (180 / vA) - 2

Substituting the value of t in equation (2):

180 = vB * ((180 / vA) - 2 + 4.5)

Simplifying the equation:

180 = vB * ((180 - 2vA) / vA + 2.5)

Cross-multiplying:

180 * vA = vB * (180 - 2vA + 2.5vA)

180vA = vB * (180 + 0.5vA)

Dividing both sides by vA:

180 = vB * (180 / vA + 0.5)

Now, we have an equation relating vA and vB. We can solve this equation to find the values of vA and vB.

Let's solve the equation:

180 = vB * (180 / vA + 0.5)

Dividing both sides by 180:

1 = vB / vA + 0.5

Subtracting 0.5 from both sides:

0.5 = vB / vA

Cross-multiplying:

vB = 0.5 * vA

Substituting the value of vB in equation (1):

180 = vA * (t + 2)

180 = vA * ((180 / vA) - 2 + 2)

Simplifying the equation:

180 = vA * (180 / vA)

180 = 180

The equation is true for any value of vA. This means that the value of vA can be any positive number.

Since vB = 0.5 * vA, the value of vB will be half of vA.

Therefore, the speed of the train starting from A can be any positive number, and the speed of the train starting from B will be half of the speed of the train starting from A.

In conclusion, the speed of each train can vary, but the speed of the train starting from B will always be half of the speed of the train starting from A.

Note: The specific values of vA and vB cannot be determined without additional information.

Answer

The speed of the train starting from A can be any positive number, and the speed of the train starting from B will be half of the speed of the train starting from A.