Question

4. Из одной деревни в противоположных направлениях вышли одновременно два пешехода. Через 7 часов расстояние между ними стало 84 км. Расстояние, которое прошел первый пешеход, на 14 км больше расстояния, которое прошел второй пешеход. Найдите скорость каждого.

Answer 1

1)   14:7=2(км/ч) - на столько скорость первого больше
2)   (84-14):2=35(км) - прошел второй
3)   35+14=49(км) - прошел первый
4)   49:7=7(км/ч) - скорость первого
5)    7-2=5(км/ч) - скорость второго..

или

х  км- прошел второй
84-х  км - прошел первый, на 14 км больше
Время в пути 7 ч

84-х -х=14
2х=84-14
2х=70
х=35(км)-прошел второй
35+14=49(км)-прошел первый

49:7=7(км/ч)-скорость первого
35:7=5(км/ч)-скорость второго

Answer 2

Problem Analysis

We have two pedestrians who start walking in opposite directions from the same village at the same time. After 7 hours, the distance between them is 84 km. The first pedestrian has traveled 14 km more than the second pedestrian. We need to find the speed of each pedestrian.

Solution

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

We know that the distance traveled by each pedestrian is equal to their speed multiplied by the time they have been walking. Therefore, we can set up the following equations:

1. Distance traveled by the first pedestrian: x * 7 km 2. Distance traveled by the second pedestrian: y * 7 km

We are also given that the distance between them after 7 hours is 84 km. So we can write the equation:

3. (x * 7) + (y * 7) = 84

We are also given that the first pedestrian has traveled 14 km more than the second pedestrian. So we can write the equation:

4. x * 7 = (y * 7) + 14

Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From equation 4, we can rewrite it as:

5. x = y + 2

Substituting equation 5 into equation 3, we get:

6. (y + 2) * 7 + (y * 7) = 84

Simplifying equation 6:

7. 7y + 14 + 7y = 84 8. 14y + 14 = 84 9. 14y = 70 10. y = 5

Substituting the value of y back into equation 5, we get:

11. x = 5 + 2 12. x = 7

Therefore, the speed of the first pedestrian is 7 km/h and the speed of the second pedestrian is 5 km/h.

Answer

The speed of the first pedestrian is 7 km/h and the speed of the second pedestrian is 5 km/h.