Question

Из пункта А в пункт В, расстояние между которыми 17 км, вышел пешеход.Через 0,5 часа навстречу ему из пункта В вышел второй пешеход и встретился с первым через 1,5 часа после своего выхода. Найдите скорость каждого пешехода, если известно, что скорость первого на 2 км/ч меньше скорости второго. Решить нужно системой уравнений.

Answer 1

Скрость первого -х км/ч Скорость второго -(х + 2)км/ч  первый шел до встречи 2 часа ( 0,5 + 1,5) Второй шел до встречи 1,5 часа  Вместе они прошли 17 км  х * 2 + (x +2) * 1,5 = 17  3,5х + 3 = 17  3,5 x = 14  x = 4 км/ч -скорость первого  х + 2 = 6 км/ч -скорост- второго

Answer 2

Problem Analysis

We are given that a pedestrian starts walking from point A to point B, which are 17 km apart. After 0.5 hours, another pedestrian starts walking from point B towards point A. They meet each other 1.5 hours after the second pedestrian starts walking. We need to find the speed of each pedestrian, given that the speed of the first pedestrian is 2 km/h less than the speed of the second pedestrian.

Solution

Let's assume the speed of the second pedestrian is x km/h. Then the speed of the first pedestrian will be x - 2 km/h.

We can use the formula speed = distance / time to find the time taken by each pedestrian to meet each other.

The first pedestrian walks for 0.5 hours before meeting the second pedestrian. So, the distance covered by the first pedestrian in 0.5 hours is 0.5 * (x - 2) km.

The second pedestrian walks for 1.5 hours before meeting the first pedestrian. So, the distance covered by the second pedestrian in 1.5 hours is 1.5 * x km.

Since the total distance between the two pedestrians is 17 km, we can set up the following equation:

0.5 * (x - 2) + 1.5 * x = 17

Now, let's solve this equation to find the value of x.

Calculation

0.5 * (x - 2) + 1.5 * x = 17

Simplifying the equation:

0.5x - 1 + 1.5x = 17

2x = 17 + 1

2x = 18

x = 9

The speed of the second pedestrian is 9 km/h. Therefore, the speed of the first pedestrian is 9 - 2 = 7 km/h.

Answer

The speed of the first pedestrian is 7 km/h and the speed of the second pedestrian is 9 km/h.