Question

Расстояние между двумя железнодорожными станциями 336 км. С этих станций выехали одновременно навстречу друг другу два поезда и встретились через 2 2/5 ч. Найди скорость каждого поезда, если скорость одного из них на 5 км./ч. больше другого?

Answer 1

Пусть скорость второго поезда х км/ч,а х+5км/ч-скорость второго. Скорость сближения двух поездов- х+х+5=2х+5 км/ч. Составим уравнение: (2х+5)*2 2/5=336 2х+5=336:2 2/5 2х+5=336:12/5 2х+5=336*5/12 2х+5=140 2х=135 х=67,5км/ч-скорость второго поезда. 1)67,5+5=72,5(км/ч)-скорость первого поезда.

Answer 2

Problem Analysis

We are given that the distance between two railway stations is 336 km. Two trains start simultaneously from these stations and meet each other after 2 2/5 hours. We need to find the speed of each train, given that the speed of one train is 5 km/h greater than the other.

Solution

Let's assume the speed of one train is x km/h. Since the speed of the other train is 5 km/h greater, its speed will be (x + 5) km/h.

We can use the formula distance = speed × time to calculate the distance traveled by each train.

The first train travels for 2 2/5 hours at a speed of x km/h: Distance traveled by the first train = x × (2 2/5) km.

The second train also travels for 2 2/5 hours at a speed of (x + 5) km/h: Distance traveled by the second train = (x + 5) × (2 2/5) km.

Since the total distance between the two stations is 336 km, the sum of the distances traveled by both trains should be equal to 336 km: x × (2 2/5) + (x + 5) × (2 2/5) = 336 km.

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

Calculation

Let's calculate the value of x using the equation derived above.

x × (2 2/5) + (x + 5) × (2 2/5) = 336 km

Simplifying the equation: x × (12/5) + (x + 5) × (12/5) = 336 km

Multiplying both sides of the equation by 5 to eliminate the fractions: 5 × x × (12/5) + 5 × (x + 5) × (12/5) = 5 × 336 km

Simplifying further: 12 × x + 12 × (x + 5) = 1680 km

Expanding the equation: 12x + 12x + 60 = 1680 km

Combining like terms: 24x + 60 = 1680 km

Subtracting 60 from both sides of the equation: 24x = 1620 km

Dividing both sides of the equation by 24: x = 67.5 km/h

Now we know that the speed of one train is 67.5 km/h. The speed of the other train, which is 5 km/h greater, will be: 67.5 + 5 = 72.5 km/h.

Therefore, the speed of the first train is 67.5 km/h and the speed of the second train is 72.5 km/h.

Answer

The speed of the first train is 67.5 km/h and the speed of the second train is 72.5 km/h.