Question

От двух станций,расстояние между которыми 635 км одновременно навстречу друг другу выехали два поезда и встретились через 5 ч.Скорость одного поезда 55 км/ч Найди скорость второго поезда.(Реши задачу двумя способами

Answer 1

1 способ: 55*5=275 км за 5 часов прошел 1 поезд                                                                  635-275=360 км прошел 2 поезд                                                                              360:5=72 км/час скорость 2 поезда                                                               2 способ: 635-(55*5)=635-275=360 км прошел 2 поезд                                                           360:5=72 км/час скорость 2 поезда

Answer 2

Problem Analysis

We are given that two trains start simultaneously from two stations and meet each other after 5 hours. The distance between the two stations is 635 km, and the speed of one train is 55 km/h. We need to find the speed of the second train.

Method 1: Using Relative Speed

Let's solve the problem using the concept of relative speed. The relative speed of two objects moving towards each other is the sum of their individual speeds. In this case, the relative speed of the two trains is the sum of their speeds.

Let's denote the speed of the second train as x km/h.

The relative speed of the two trains is given by: Relative Speed = Speed of Train 1 + Speed of Train 2

Using the given information, we can set up the equation: 55 km/h + x km/h = Relative Speed

Since the trains meet after 5 hours, we can use the formula: Distance = Speed × Time

The distance covered by the first train is: Distance = Speed of Train 1 × Time = 55 km/h × 5 h = 275 km

The distance covered by the second train is also 275 km, as the total distance between the two stations is 635 km and the trains meet in the middle.

Using the formula for distance, we can set up another equation: Distance = Speed of Train 2 × Time = x km/h × 5 h = 275 km

Now we have two equations: 55 km/h + x km/h = Relative Speed x km/h × 5 h = 275 km

We can solve these equations simultaneously to find the value of x.

Method 2: Using Time and Distance

Alternatively, we can solve the problem using the concept of time and distance. The time taken by both trains to meet each other is the same, as they start simultaneously. Let's denote this time as t hours.

The distance covered by the first train is: Distance = Speed of Train 1 × Time = 55 km/h × t h

The distance covered by the second train is: Distance = Speed of Train 2 × Time = x km/h × t h

Since the total distance between the two stations is 635 km, we can set up the equation: Distance covered by Train 1 + Distance covered by Train 2 = Total Distance 55 km/h × t h + x km/h × t h = 635 km

We also know that the trains meet after 5 hours, so we can set up another equation: t h = 5 h

Now we have two equations: 55 km/h × t h + x km/h × t h = 635 km t h = 5 h

We can solve these equations simultaneously to find the value of x.

Solution

Let's solve the problem using both methods.

Method 1: Using Relative Speed

Using the equation for relative speed: 55 km/h + x km/h = Relative Speed

Since the trains meet after 5 hours, the distance covered by each train is 275 km.

Using the equation for distance: Distance = Speed × Time

For the first train: 55 km/h × 5 h = 275 km

For the second train: x km/h × 5 h = 275 km

Simplifying the equations: 275 km = 275 km 5x = 275

Dividing both sides by 5: x = 55

Therefore, the speed of the second train is 55 km/h.

Method 2: Using Time and Distance

Using the equation for distance: 55 km/h × t h + x km/h × t h = 635 km

Since the trains meet after 5 hours, the time taken by both trains is 5 hours.

Substituting the value of t: 55 km/h × 5 h + x km/h × 5 h = 635 km

Simplifying the equation: 275 km + 5x km = 635 km

Subtracting 275 km from both sides: 5x km = 360 km

Dividing both sides by 5: x = 72

Therefore, the speed of the second train is 72 km/h.

Conclusion

Using two different methods, we have found that the speed of the second train can be either 55 km/h or 72 km/h.