Question

Решите задачу двумя способами. Расстояние между станциями 350 км. От этих станций одновременно навстречу друг другу отправились два поездаю Они встретились через 2,5 чю Определите скорость первого поезда, если скорость второго 65 км/ч

Answer 1

1 способ

350:2.5=140км/ч скорость сближения 

140-65=75км/ч скорость первого поезда

 

2 способ

65*2.5=162.5км проехал второй поезд

350-162.5=187.5км проехал первый поезд

187.5:2.5=75км/ч скорость первого поезда

Answer 2

Problem Analysis

We are given that two trains start simultaneously from two stations and meet each other after 2.5 hours. The distance between the stations is 350 km, and the speed of the second train is 65 km/h. We need to determine the speed of the first train.

Method 1: Using Relative Speed

To solve this problem, we can consider the relative speed of the two trains. When two objects are moving towards each other, their relative speed 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 first train as x km/h. The relative speed of the two trains is then x + 65 km/h. We know that the trains meet after 2.5 hours, and the distance between them is 350 km. We can use the formula:

Distance = Speed × Time

Substituting the values, we have:

350 = (x + 65) × 2.5

Simplifying the equation, we get:

350 = 2.5x + 162.5

Now, we can solve for x:

2.5x = 350 - 162.5

2.5x = 187.5

x = 187.5 / 2.5

x = 75

Therefore, the speed of the first train is 75 km/h.

Method 2: Using Time and Distance

Alternatively, we can solve this problem by considering the time taken by each train to cover the distance between the stations.

Let's denote the speed of the first train as x km/h. We know that the second train has a speed of 65 km/h. The time taken by the first train to cover the distance is 350 / x hours, and the time taken by the second train is 2.5 hours.

Since the trains meet after 2.5 hours, we can set up the equation:

350 / x = 2.5

To solve for x, we can cross-multiply:

350 = 2.5x

Now, we can solve for x:

x = 350 / 2.5

x = 140

Therefore, the speed of the first train is 140 km/h.

Conclusion

Using two different methods, we have determined that the speed of the first train is either 75 km/h (using relative speed) or 140 km/h (using time and distance).