Question

Из двух сёл, расстояние между которыми 38 км, одновременно, навстречу друг другу вышли два пешехода. Скорость одного из них равна 4 целых 4/9, что в 1 целую 1/9 раза больше скорости второго. Через сколько времени они встретятся?

Answer 1

4 4/9:1 1/9=40/9:10/9=4 (км/ч) скорость второго
4+4 4/9=8 4/9 (км/ч) скорость сближения
38:8 4/9=38: 76/9=9/2=4 1/2=4,5 (ч)
Ответ: они встретятся через 4,5 часа (через 4 часа 30 минут)

Answer 2

Problem Analysis

We are given that there are two villages with a distance of 38 km between them. Two pedestrians start walking towards each other simultaneously. The speed of one pedestrian is 4 4/9, which is 1 1/9 times the speed of the other pedestrian. We need to find out how much time it will take for them to meet.

Solution

Let's assume the speed of the slower pedestrian is x km/h. Then, the speed of the faster pedestrian will be (1 1/9)x km/h.

We can use the formula distance = speed × time to find the time it takes for them to meet. The total distance they need to cover is 38 km.

Let's denote the time taken by the slower pedestrian as t hours. Then, the time taken by the faster pedestrian will be t hours as well.

The distance covered by the slower pedestrian in t hours is x × t km, and the distance covered by the faster pedestrian in t hours is (1 1/9)x × t km.

According to the problem, the sum of these distances should be equal to 38 km:

x × t + (1 1/9)x × t = 38

Simplifying the equation, we get:

x × t + (10/9)x × t = 38

Multiplying both sides of the equation by 9 to eliminate the fraction, we get:

9x × t + 10x × t = 342

Combining like terms, we have:

19x × t = 342

Dividing both sides of the equation by 19t, we get:

x = 342 / (19t)

Now, we can substitute this value of x into the equation x × t + (1 1/9)x × t = 38 to solve for t.

342 / (19t) × t + (10/9) × 342 / (19t) × t = 38

Simplifying the equation, we get:

342 + (10/9) × 342 = 38 × 19t

Multiplying both sides of the equation by 9/10 to eliminate the fraction, we get:

342 × (9/10) + 342 = 38 × 19t

Simplifying the equation, we have:

308 + 342 = 722t

Adding the numbers on the left side, we get:

650 = 722t

Dividing both sides of the equation by 722, we get:

t = 650 / 722

Simplifying the fraction, we have:

t ≈ 0.901

Therefore, it will take approximately 0.901 hours for the pedestrians to meet.

Answer

The pedestrians will meet in approximately 0.901 hours.

Note: The above solution assumes that the pedestrians are walking at a constant speed throughout the journey.