Question

Из пункта A и B навстречу друг другу выехали одновременно два автомобиля, которые двигались равномерно и без остановок. Известно, что первый автомобиль ехал из A в B 8 часов, а второй автомобиль ехал из B в A 9 часов. Могли ли они встретиться через 4 часа после выезда?

Answer 1

Не могди, т.к. первый проехал за 4 часа половину пути: 4/8=0,5, а второму, чтобы проехать надо 9/2=4,5 часа...

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Answer 2

Problem Analysis

We have two cars, one traveling from point A to point B and the other traveling from point B to point A. The first car takes 8 hours to travel from A to B, while the second car takes 9 hours to travel from B to A. We need to determine if they could have met after 4 hours.

Solution

To determine if the two cars could have met after 4 hours, we need to compare the distances they have traveled.

Let's assume that the distance between A and B is x.

The first car, traveling from A to B, takes 8 hours to cover the distance x. Therefore, its speed can be calculated as x/8.

The second car, traveling from B to A, takes 9 hours to cover the same distance x. Therefore, its speed can be calculated as x/9.

After 4 hours, the first car would have traveled a distance of (x/8) * 4 and the second car would have traveled a distance of (x/9) * 4.

To determine if they could have met, we need to check if the sum of the distances traveled by both cars is equal to the total distance between A and B.

If (x/8) * 4 + (x/9) * 4 = x, then the two cars could have met after 4 hours.

Let's calculate and check if the equation holds true.

Calculation

Let's calculate the equation (x/8) * 4 + (x/9) * 4 = x.

Simplifying the equation, we get (4x/8) + (4x/9) = x.

Combining the fractions, we get (36x + 32x) / 72 = x.

Simplifying further, we get 68x / 72 = x.

Cross-multiplying, we get 68x = 72x.

Subtracting 68x from both sides, we get 4x = 0.

Since 4x = 0 is not possible, we can conclude that the equation (x/8) * 4 + (x/9) * 4 = x does not hold true.

Therefore, the two cars could not have met after 4 hours.

Answer

No, the two cars could not have met after 4 hours.