Question

Два поезда вышли навстречу друг другу одновременно с двух станций,расстояние между которыми 520 км.Через какое время расстояние между поездами будет равно 65 км,если скорость поездов 60 км/ч и 70 км/ч? РЕШИТЬ УРАВНЕНИЕМ С ОБЪЯСНЕНИЕМ

Answer 1

Х-время в пути
Расстояние=скорость*время
60*х+65+70*х=520
Х=3.5

Answer 2

Problem Analysis

We have two trains traveling towards each other from two different stations. The distance between the stations is 520 km. The speeds of the trains are 60 km/h and 70 km/h. We need to find the time it takes for the distance between the trains to be 65 km.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's assume that the time it takes for the distance between the trains to be 65 km is t hours.

The distance traveled by the first train in t hours is 60t km, and the distance traveled by the second train in t hours is 70t km.

According to the problem, the sum of the distances traveled by both trains should be equal to the distance between the stations, which is 520 km.

So, we can set up the equation: 60t + 70t = 520.

Now, let's solve this equation to find the value of t.

Calculation

Simplifying the equation: 130t = 520.

Dividing both sides of the equation by 130: t = 520 / 130.

Calculating the value of t: t = 4.

Therefore, it will take 4 hours for the distance between the trains to be 65 km.

Answer

The time it takes for the distance between the trains to be 65 km is 4 hours.

Verification

Let's verify the answer using the given information.

The first train travels at a speed of 60 km/h, so in 4 hours, it will travel a distance of 60 × 4 = 240 km.

The second train travels at a speed of 70 km/h, so in 4 hours, it will travel a distance of 70 × 4 = 280 km.

The sum of the distances traveled by both trains is 240 + 280 = 520 km, which is equal to the distance between the stations.

Therefore, the answer is verified.

Conclusion

The time it takes for the distance between the trains to be 65 km is 4 hours.