Question

Два поезда вышли одновременно с двух станций навстречу друг другу. Скорость одного равна 56 2/5 км/ч, а скорость другого - на 25% больше скорости первого. Поезда встретились , когда второй поезд прошел 141 км. Найдите расстояние между станциями.

Answer 1

1) 56 2/5*0,25=14,1(км/ч)-на столько скорость второго больше скорости первого.
2) 56 2/5+14,1=70,5(км/ч)-скорость второго поезда.
3) 141:70,5=2(ч)-через столько поезда встретились.
4) 56 2/5*2=112,8(км)-проехал первый поезд до встречи.
5) 141+112,8=253,8(км)-расстояние между станциями.
Ответ: 253.8 км.

Answer 2

Problem Analysis

We are given two trains that start simultaneously from two different stations and are moving towards each other. The speed of one train is 56 2/5 km/h, while the speed of the other train is 25% faster than the first train. The trains meet when the second train has traveled 141 km. We need to find the distance between the two stations.

Solution

Let's denote the speed of the first train as x km/h. The speed of the second train is 25% faster than the first train, so its speed is 1.25x km/h.

We know that the second train has traveled 141 km when the trains meet. We can use this information to set up an equation:

Distance traveled by the first train + Distance traveled by the second train = Total distance between the stations

Let's calculate the distance traveled by each train:

- Distance traveled by the first train = x * t (where t is the time taken for the trains to meet) - Distance traveled by the second train = 1.25x * t

The total distance between the stations is the sum of the distances traveled by each train:

x * t + 1.25x * t = Total distance

We also know that the second train has traveled 141 km when the trains meet:

1.25x * t = 141

Now we can solve this equation to find the value of t:

t = 141 / 1.25x

To find the total distance between the stations, we can substitute the value of t back into the equation:

Total distance = x * t + 1.25x * t = x * (141 / 1.25x) + 1.25x * (141 / 1.25x) = 141 + 1.25x

Now we need to find the value of x. We are given that the speed of the first train is 56 2/5 km/h. We can convert this mixed fraction to an improper fraction:

56 2/5 = (5 * 56 + 2) / 5 = 282 / 5

So, x = 282 / 5 km/h.

Now we can substitute the value of x into the equation for the total distance:

Total distance = 141 + 1.25 * (282 / 5)

Let's calculate the total distance:

Total distance = 141 + 1.25 * (282 / 5) = 141 + 1.25 * 56.4 = 141 + 70.5 = 211.5 km

Therefore, the distance between the two stations is 211.5 km.

Answer

The distance between the two stations is 211.5 km.