Question

Из двух городов, расстояние между которыми 918 км, вышли одновременно навстречу друг другу два скорых поезда. Скорость одного поезда 65 км/ч. Определи скорость другого поезда, если поезда встретились через 6 часов.

Answer 1

1) 918 : 6 =153 км/ч скорость сближения

2) 153 - 65 = 88 км/ч скорость 2 поезда

Answer 2

Problem Analysis

We are given that two trains start simultaneously from two cities that are 918 km apart and are moving towards each other. The speed of one train is given as 65 km/h. We need to determine the speed of the other train, given that the trains meet after 6 hours.

Solution

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

We know that the distance covered by the first train in 6 hours is equal to the distance covered by the second train in 6 hours. Since the trains are moving towards each other, the sum of the distances covered by both trains will be equal to the total distance between the cities.

The distance covered by the first train in 6 hours is given by: Distance1 = Speed1 * Time = 65 km/h * 6 hours

The distance covered by the second train in 6 hours is given by: Distance2 = Speed2 * Time = x km/h * 6 hours

Since the sum of the distances covered by both trains is equal to the total distance between the cities, we can write the equation: Distance1 + Distance2 = Total Distance

Substituting the values, we get: 65 km/h * 6 hours + x km/h * 6 hours = 918 km

Simplifying the equation, we have: 390 km + 6x km = 918 km

Now, we can solve this equation to find the value of x.

Calculation

Let's solve the equation: 390 km + 6x km = 918 km

Subtracting 390 km from both sides, we get: 6x km = 918 km - 390 km

Simplifying, we have: 6x km = 528 km

Dividing both sides by 6 km, we get: x = 528 km / 6 km

Calculating the value, we have: x = 88 km/h

Answer

Therefore, the speed of the second train is 88 km/h.

Verification

Let's verify the answer using the given information.

The distance covered by the first train in 6 hours is: Distance1 = Speed1 * Time = 65 km/h * 6 hours = 390 km

The distance covered by the second train in 6 hours is: Distance2 = Speed2 * Time = 88 km/h * 6 hours = 528 km

The sum of the distances covered by both trains is: Distance1 + Distance2 = 390 km + 528 km = 918 km

As we can see, the total distance between the cities is indeed 918 km, which confirms that the answer is correct.

Conclusion

The speed of the second train is 88 km/h.