Question

От станции А до станции В поезд проехал за 1,9 часа. От станции B до станции A электричка проехала за 2,5 часа. Известно, что электричка шла на 24 км/ч медленнее, чем поезд. Определи скорость поезда и скорость электр ички.​

Answer 1

Ответ:

скорость электрички — 76 км/ч; скорость поезда — 100 км/ч.

Объяснение:

скорость электрички — x км/ч⇒S=2,5x км

скорость поезда — x+24 км/ч⇒S=1,9(x+24) км

2,5x=1,9(x+24)

2,5x=1,9x+45,6

2,5x-1,9x=45,6

0,6x=45,6

x=45,6:0,6

x=76 (км/ч) скорость электрички

x+24=76+24=100 (км/ч) скорость поезда

Answer 2

Problem Analysis

We are given the following information: - The train traveled from station A to station B in 1.9 hours. - The train traveled from station B to station A in 2.5 hours. - The train was 24 km/h faster than the electric train.

We need to determine the speed of the train and the speed of the electric train.

Solution

Let's assume the speed of the train is x km/h and the speed of the electric train is y km/h.

From the given information, we can set up the following equations:

Equation 1: The train traveled from station A to station B in 1.9 hours. Distance = Speed × Time x × 1.9 = AB (Equation 1)

Equation 2: The train traveled from station B to station A in 2.5 hours. Distance = Speed × Time x × 2.5 = BA (Equation 2)

Equation 3: The train was 24 km/h faster than the electric train. x = y + 24 (Equation 3)

To solve this system of equations, we can substitute Equation 3 into Equations 1 and 2.

Substituting Equation 3 into Equation 1: (y + 24) × 1.9 = AB (Equation 4)

Substituting Equation 3 into Equation 2: (y + 24) × 2.5 = BA (Equation 5)

Now we have two equations (Equations 4 and 5) with two unknowns (AB and BA). We can solve these equations to find the values of AB and BA.

Let's solve the equations:

Solution Steps

1. Substitute Equation 3 into Equations 1 and 2: - Equation 4: (y + 24) × 1.9 = AB - Equation 5: (y + 24) × 2.5 = BA

2. Simplify the equations: - Equation 4: 1.9y + 45.6 = AB - Equation 5: 2.5y + 60 = BA

3. Rearrange the equations to isolate AB and BA: - Equation 4: AB = 1.9y + 45.6 - Equation 5: BA = 2.5y + 60

4. Set AB and BA equal to each other since they represent the same distance: - 1.9y + 45.6 = 2.5y + 60

5. Solve for y: - Subtract 1.9y from both sides: 45.6 = 0.6y + 60 - Subtract 60 from both sides: -14.4 = 0.6y - Divide both sides by 0.6: y = -14.4 / 0.6 - Simplify: y = -24

6. Substitute the value of y back into Equation 3 to find x: - Equation 3: x = y + 24 - Substitute y = -24: x = -24 + 24 - Simplify: x = 0

Answer

The speed of the train is 0 km/h and the speed of the electric train is -24 km/h.

Please note that a negative speed for the electric train indicates that it is traveling in the opposite direction compared to the train.