Question

Из двух городов , расстояние между которыми 960 км, навстречу друг другу в 8 ч утра вышли два поезда. Они встретились в 6 ч вечера того же дня. Найдите скорость первого поезда, если скорость второго 40 км/ч.

Answer 1

Пусть скорость 1поезда будет х км/час, проехали они с 8 до 6 вечера 10 часов, 10х(расстояние прошёл первый поезд), 10*40(расстояние прошёл 2поезд), составляем уравнение 10х+10*40=960, 10х=960-400,10х=560,х=56км/час скорость первого поезда

Answer 2

Problem Analysis

We are given that two trains, traveling towards each other, departed from two cities that are 960 km apart at 8:00 AM. The trains met at 6:00 PM on the same day. We need to find the speed of the first train, given that the speed of the second train is 40 km/h.

Solution

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

To find the speed of the first train, we can use the formula: Distance = Speed × Time

The distance traveled by the first train can be calculated as: Distance = Speed × Time

The distance traveled by the second train can also be calculated as: Distance = Speed × Time

Since the two trains are traveling towards each other, the sum of their distances should be equal to the total distance between the two cities, which is 960 km.

So we have the equation: Distance of first train + Distance of second train = Total distance

Substituting the values, we get: (x km/h × 10 hours) + (40 km/h × 10 hours) = 960 km

Simplifying the equation, we have: 10x + 400 = 960

Solving for x, we get: 10x = 960 - 400 10x = 560 x = 560 / 10 x = 56

Therefore, the speed of the first train is 56 km/h.

Answer

The speed of the first train is 56 km/h.

Verification

Let's verify the answer using the given information.

The distance traveled by the first train can be calculated as: Distance = Speed × Time Distance = 56 km/h × 10 hours Distance = 560 km

The distance traveled by the second train can be calculated as: Distance = Speed × Time Distance = 40 km/h × 10 hours Distance = 400 km

The sum of the distances traveled by both trains is: 560 km + 400 km = 960 km

The total distance between the two cities is indeed 960 km, which confirms that the answer is correct.

Conclusion

The speed of the first train is 56 km/h.