Question

Решите пожалуйста задачу:Два пешехода шли навстречу друг другу и в пути встретились. Через 5/12 ( пять двенадцатых) ч после их встречи расстояние между ними стало равным 3 3/4( три целых три четвёртых) км.С какой скоростью движется первый пешеход, если скорость второго равна 3 км/ч?По действиям))

Answer 1

3 3/4= 15/4

15/4:5/12=15/4* 12/5=3/4*12=3-3=9 км/ч- суммарная скорость обоих
9-3=6 км/ч скорость первого

Answer 2

Problem Analysis

We are given that two pedestrians are walking towards each other. After meeting, the distance between them becomes 3 3/4 km. We are also given that the second pedestrian is walking at a speed of 3 km/h. We need to find the speed of the first pedestrian.

Solution

Let's assume the speed of the first pedestrian is x km/h.

The time taken by the first pedestrian to cover the initial distance is the same as the time taken by the second pedestrian to cover the same distance. This can be expressed as:

Distance / Speed = Time

The initial distance covered by both pedestrians is the sum of the distances covered by each pedestrian before they meet. Since they are walking towards each other, the sum of their distances is the total distance between them before they meet.

Let's calculate the initial distance covered by the first pedestrian:

Initial distance covered by the first pedestrian = (5/12) * x

The initial distance covered by the second pedestrian is:

Initial distance covered by the second pedestrian = (5/12) * 3

The total initial distance between the pedestrians is the sum of these two distances:

Total initial distance = (5/12) * x + (5/12) * 3

After they meet, the distance between them becomes 3 3/4 km. We can convert this mixed fraction to an improper fraction:

3 3/4 = (4 * 3 + 3) / 4 = 15/4

The final distance between the pedestrians is:

Final distance = 15/4

Since the time taken by both pedestrians to cover the initial distance is the same, we can set up the following equation:

(Total initial distance) / (Speed of the first pedestrian) = (Final distance) / (Speed of the second pedestrian)

Substituting the values we calculated earlier:

[(5/12) * x + (5/12) * 3] / x = 15/4 / 3

Simplifying the equation:

[(5/12) * x + 15/12] / x = 15/12 / 3

[(5/12) * x + 15/12] / x = 5/4

Cross-multiplying:

4 * [(5/12) * x + 15/12] = 5 * x

Simplifying:

(5/3) * x + 5 = 5 * x

5/3 * x - 5 * x = -5

-10/3 * x = -5

Dividing both sides by -10/3:

x = (-5) / (-10/3)

Simplifying:

x = 3/2

Therefore, the speed of the first pedestrian is 3/2 km/h.

Answer

The speed of the first pedestrian is 3/2 km/h.