Question

Помогите пожалуйста срочно решить задачу: Из двух городов, расстояние между которыми 427 км , одновременно навстречу друг другу вышли два поезда. Скорость одного 52 км/ч, что на 5 км/ч меньше, чем скорость другого. Через сколько часов они будут на расстоянии 82 км друг от друга? Даю по 15 баллов.

Answer 1

Скорость 2 поезда
1)52 км/ч + 5=57 км/ч
складываем две скорости так как они едут на встречу
2)52+57=109(км/ч)-два поезда за час
3)109*3=327(км)-за 3часа
4)427-327=100(км)-останется
5)100-82=18(км)
6)109:60=1.8(км)-за минуту
7)18:1.8=10(мин)
Ответ:Через 3часа 10 минут

Answer 2

Problem Analysis

We are given that two trains are traveling towards each other from two cities, and we need to determine how long it will take for them to be 82 km apart. The speed of one train is 52 km/h, which is 5 km/h less than the speed of the other train. We can solve this problem by setting up an equation based on the relative speeds of the two trains.

Solution

Let's assume the speed of the faster train is x km/h. Then the speed of the slower train is x - 5 km/h.

We can use the formula distance = speed × time to set up an equation.

The distance traveled by the faster train is x × t (where t is the time in hours), and the distance traveled by the slower train is (x - 5) × t.

According to the problem, the sum of the distances traveled by the two trains is equal to the total distance between the cities, which is 427 km.

So we have the equation: x × t + (x - 5) × t = 427.

Simplifying the equation, we get: 2x × t - 5 × t = 427.

Combining like terms, we have: (2x - 5) × t = 427.

To find the time it takes for the trains to be 82 km apart, we can substitute the distance as 82 km into the equation and solve for t.

Let's solve the equation:

(2x - 5) × t = 427.

Substituting the distance as 82 km:

(2x - 5) × t = 82.

Now we can solve for t.

Calculation

To solve for t, we need to find the value of x first. We can do this by rearranging the equation (2x - 5) × t = 427 and solving for x.

(2x - 5) × t = 427.

Dividing both sides of the equation by t:

2x - 5 = 427 ÷ t.

Adding 5 to both sides of the equation:

2x = 427 ÷ t + 5.

Dividing both sides of the equation by 2:

x = (427 ÷ t + 5) ÷ 2.

Now we can substitute the value of x into the equation (2x - 5) × t = 82 and solve for t.

((427 ÷ t + 5) ÷ 2) × t = 82.

Simplifying the equation:

(427 ÷ t + 5) × t = 164.

Expanding the equation:

427 × t ÷ t + 5 × t = 164.

Simplifying further:

427 + 5t = 164.

Subtracting 427 from both sides of the equation:

5t = 164 - 427.

Simplifying:

5t = -263.

Dividing both sides of the equation by 5:

t = -263 ÷ 5.

Calculating:

t = -52.6.

Since time cannot be negative, we can conclude that there is no solution to this problem.

Conclusion

Based on the given information, there is no solution to the problem. The trains will not be 82 km apart from each other. It is possible that there is an error in the problem statement or the given information. Please double-check the problem and the values provided.