Question

Из одного пункта в противоположных направлениях выехали два поезда. Если они будут ехать 3,2 ч, то расстояние между ними будет 480 км. Если первый поезд выедет на 1,4 ч раньше второго, то после этого между ними через 2 ч расстояние будет 412 км. Найдите скорость каждого поезда

Answer 1

Обозначим скорости поездов за х и утогда можно записать (х + у)*3,2=480 х + у=480:3,2 х + у=150 ⇒ у=150-хзапишим второе условие задачи (1,4+2)*х +2*у=412 подставим в уравнение значение у 3,4 х +2*(150-х)=4123,2 х +300-2 х=4121,4 х=112 х=112:1,4 х=80 км/ч у=150-80 у=70 км/ч

Answer 2

Problem Analysis

We have two trains that start from the same point and travel in opposite directions. The distance between them after traveling for 3.2 hours is 480 km. If the first train starts 1.4 hours earlier than the second train, the distance between them after 2 hours is 412 km. We need to find the speed of each train.

Solution

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

To find the speed of each train, we can use the formula: speed = distance / time.

# Calculation 1

After traveling for 3.2 hours, the distance between the trains is 480 km. Using the formula, we can write the equation: x * 3.2 + y * 3.2 = 480.

# Calculation 2

After the first train starts 1.4 hours earlier than the second train, the distance between them after 2 hours is 412 km. Using the formula, we can write the equation: x * 2 + y * 2 = 412.

Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solution Steps

1. Solve the system of equations using any method (substitution, elimination, etc.) to find the values of x and y. 2. Substitute the values of x and y back into the original equations to verify the solution.

Let's solve the system of equations to find the speeds of the trains.

Solution

To solve the system of equations, we can use the substitution method.

From Calculation 1, we have: x * 3.2 + y * 3.2 = 480.

From Calculation 2, we have: x * 2 + y * 2 = 412.

We can rewrite Calculation 1 as: 3.2x + 3.2y = 480.

Now, let's solve the system of equations:

Step 1: Solve Calculation 2 for x: x = (412 - 2y) / 2.

Step 2: Substitute the value of x in Calculation 1: 3.2((412 - 2y) / 2) + 3.2y = 480.

Step 3: Simplify the equation: (412 - 2y) + 3.2y = 480.

Step 4: Solve for y: 412 - 2y + 3.2y = 480.

Step 5: Simplify and solve for y: 1.2y = 68.

Step 6: Divide both sides by 1.2 to solve for y: y = 68 / 1.2.

Step 7: Calculate the value of y: y = 56.67.

Step 8: Substitute the value of y back into Calculation 2 to solve for x: x * 2 + 56.67 * 2 = 412.

Step 9: Simplify and solve for x: 2x + 113.34 = 412.

Step 10: Subtract 113.34 from both sides to solve for x: 2x = 412 - 113.34.

Step 11: Simplify and solve for x: 2x = 298.66.

Step 12: Divide both sides by 2 to solve for x: x = 298.66 / 2.

Step 13: Calculate the value of x: x = 149.33.

Therefore, the speed of the first train is 149.33 km/h and the speed of the second train is 56.67 km/h.

Answer

The speed of the first train is 149.33 km/h and the speed of the second train is 56.67 km/h.