Question

Из двух пунктов , расстояние между которыми 210 км.Вышли одновременно навстречу друг другу два электропоезда.Скорость одного из них на 5км/x больше скорости другого.Найдите Скорость каждого электропоезда,если они встретились через 2ч после своего выхода.

Answer 1

х (км/ч) - скорость 1-го поезда

х+5 (км/ч) - скорость 2-го поезда

1) 210:2=105 (км/ч) - скорость сближения поездов

2) х+х+5=105

   2х=100

   х=50 (км/ч) - скорость одного поезда

   50+5=55 (км/ч) - скорость второго поезда

Answer 2

Problem Analysis

We are given two trains that start simultaneously and travel towards each other. The distance between them is 210 km. The speed of one train is 5 km/h greater than the speed of the other train. We need to find the speed of each train if they meet after 2 hours.

Solution

Let's assume the speed of the slower train is x km/h. Then the speed of the faster train will be x + 5 km/h.

We can use the formula distance = speed × time to find the distance traveled by each train in 2 hours.

For the slower train: - Distance = Speed × Time - Distance = x km/h × 2 h - Distance = 2x km

For the faster train: - Distance = Speed × Time - Distance = (x + 5) km/h × 2 h - Distance = 2(x + 5) km

Since the total distance between the trains is 210 km, we can set up the following equation: - Distance of slower train + Distance of faster train = Total distance - 2x + 2(x + 5) = 210

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

Calculation

Let's solve the equation:

2x + 2(x + 5) = 210

Simplifying the equation:

2x + 2x + 10 = 210 4x + 10 = 210 4x = 200 x = 50

The speed of the slower train is 50 km/h. The speed of the faster train is 50 + 5 = 55 km/h.

Answer

The speed of the slower train is 50 km/h and the speed of the faster train is 55 km/h.

Explanation

The slower train travels at a speed of 50 km/h and the faster train travels at a speed of 55 km/h. After 2 hours, the slower train will have traveled a distance of 2 × 50 = 100 km, and the faster train will have traveled a distance of 2 × 55 = 110 km. The total distance traveled by both trains is 100 km + 110 km = 210 km, which is the distance between them when they meet.