Question

Два поезда вышли одновременно навстречу друг другу. первый поезд двигался со скоростью 72 км/ч,а второй 68 км/ч.Второй поезд прошёл до встречи 408 км.Какое расстояние до встречи прошёл первый поезд ?

Answer 1

1)408:68=6(часов)-время в пути до встречи
2)6*72=432(км)- расстояние, пройденное первым поездом
Ответ: 432 км

Answer 2

Problem Analysis

We are given two trains that start simultaneously and are moving towards each other. The first train is traveling at a speed of 72 km/h, and the second train is traveling at a speed of 68 km/h. We need to determine the distance traveled by the first train before the two trains meet.

Solution

To solve this problem, we can use the formula:

Distance = Speed × Time

Let's assume that the first train traveled a distance of x km before the two trains met. Since the second train traveled a distance of 408 km before the meeting point, the total distance covered by both trains is the sum of their individual distances:

x + 408 = Distance

We can calculate the time taken by each train to cover their respective distances using the formula:

Time = Distance / Speed

For the first train: Time1 = x / 72

For the second train: Time2 = 408 / 68

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

x / 72 = 408 / 68

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

Calculation

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

x / 72 = 408 / 68

Cross-multiplying, we get:

68x = 72 × 408

Simplifying, we have:

68x = 29376

Dividing both sides by 68, we find:

x = 432

Answer

Therefore, the first train traveled a distance of 432 km before the two trains met.

Verification

To verify our answer, let's substitute the value of x into the equation:

x + 408 = Distance

432 + 408 = Distance

840 = Distance

Now, let's calculate the time taken by each train:

For the first train: Time1 = x / 72 = 432 / 72 = 6 hours

For the second train: Time2 = 408 / 68 = 6 hours

Since both trains took the same time to meet, our answer is correct.

Conclusion

The first train traveled a distance of 432 km before the two trains met.