Question

. Два поезда вышли одновременно с двух станций навстречу друг другу. Скорость одного- 56,4 км/ч, а другого- на 25% меньше. Найти расстояние между станциями, если второй до встречи прошел 141 км.

Answer 1

Скорость второго 56,4-(56,4*25%)=56,4-14,1=42,3 км/ч
время, которое прошло до встречи 141 : 42,3=10/3=3 1/3 часа
расстояние, которое прошел первый поезд до встречи  3 1/3 * 56,4 = 188 км
общее расстояние между станциями 141 + 188=329 км
Ответ. 329 км.

Answer 2

1)25% = 0,25
56,4 * 0,25 = 14,1(км/ч)  составляют 25%
2) 56,4 - 14,1 = 42,3 (км/ч) - скорость второго поезда
3) 141 : 42,3 = 3 1/3 (часа) - через это время поезда встретились
4) 56,4 * 3 1/3 =  188 (км) прошёл 1-ый поезд до встречи
5) 141 + 188 = 329 (км)
Ответ: 329 км расстояние между станциями.

Answer 3

Problem Analysis

We have two trains traveling towards each other from two different stations. The speed of one train is 56.4 km/h, while the speed of the other train is 25% less. We need to find the distance between the two stations, given that the second train traveled 141 km before the meeting.

Solution

Let's assume the distance between the two stations is d km.

The first train's speed is 56.4 km/h, so the time it takes for the first train to reach the meeting point is t1 = d / 56.4 hours.

The second train's speed is 25% less than the first train's speed, which means its speed is 0.75 * 56.4 = 42.3 km/h. The time it takes for the second train to reach the meeting point is t2 = 141 / 42.3 hours.

Since both trains started at the same time, the total time taken for both trains to meet is the same. Therefore, we can equate the two time expressions:

t1 = t2

Substituting the values of t1 and t2:

d / 56.4 = 141 / 42.3

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

Calculation

Let's calculate the value of d using the equation:

d / 56.4 = 141 / 42.3

Multiplying both sides of the equation by 56.4:

d = (141 / 42.3) * 56.4

Calculating the value of d:

d ≈ 188.8 km

Answer

The distance between the two stations is approximately 188.8 km.

Verification

Let's verify the answer using the given information.

The first train's speed is 56.4 km/h, and the second train's speed is 25% less, which is approximately 42.3 km/h. The second train traveled 141 km before the meeting.

The time taken by the first train to reach the meeting point is t1 = d / 56.4 ≈ 188.8 / 56.4 ≈ 3.35 hours.

The time taken by the second train to reach the meeting point is t2 = 141 / 42.3 ≈ 3.34 hours.

As we can see, both trains took approximately the same time to reach the meeting point, which confirms that the distance between the two stations is approximately 188.8 km.

Conclusion

The distance between the two stations is approximately 188.8 km.