Question

Товарный поезд за 5 ч проходит расстояние на 27 км меньше чем пассажирный за 4 ч. Найдите скорость пассажирного поезда если она на 18 км/ч больше скорости товарного

Answer 1

Problem Analysis

We are given that a freight train covers a distance in 5 hours that is 27 km less than the distance covered by a passenger train in 4 hours. We need to find the speed of the passenger train, given that it is 18 km/h faster than the speed of the freight train.

Solution

Let's assume the speed of the freight train is x km/h. Therefore, the speed of the passenger train is x + 18 km/h.

We can use the formula speed = distance / time to calculate the distances covered by both trains.

The distance covered by the freight train in 5 hours is 5x km, and the distance covered by the passenger train in 4 hours is 4(x + 18) km.

According to the problem, the distance covered by the freight train is 27 km less than the distance covered by the passenger train. Therefore, we can set up the following equation:

5x = 4(x + 18) + 27

Now, let's solve this equation to find the value of x.

Calculation

Expanding the equation:

5x = 4x + 72 + 27

Combining like terms:

5x = 4x + 99

Subtracting 4x from both sides:

x = 99

Answer

The speed of the freight train is 99 km/h. Since the speed of the passenger train is 18 km/h faster, the speed of the passenger train is 99 + 18 = 117 km/h.

Therefore, the speed of the passenger train is 117 km/h.