Question

Из пункта А в пункт В. расстоянием между которыми 19 км, вышел пешеход. Через полчаса навстречу ему из пункта В вышел турист и встретил пешехода в 9 км от пункта В. Турист шел со скоростью, на 1 км/ч большей, чем пешеход. Найдите скорость пешехода, шедшего из А. С объяснением, плиз...

Answer 1

Пусть скорость пешехода х км/ч, тогда скорость туриста (х+1) км/ч. Так как встреча произошла в 9 км от В, то время он затратил $\frac{9}{x+1}$ (ч). Пешеход же прошел до встречи 19 - 9 = 10 (км). Значит затратил времени $\frac{10}{x}$ (ч). Пешеход вышел на  полчаса раньше, поэтому составим уравнение:$\frac{10}{x}-\frac{9}{x+1}=\frac{1}{2}\\\frac{10(x+1)-9x}{x(x+1)}=\frac{1}{2}\\\frac{10x+10-9x}{x^{2}+x}=\frac{1}{2}\\(x+10)2=x^{2}+x\\x^{2}+x-2x-20=0\\x^{2}-x-20=0\\D=1+80=81=9^{2}\\x_{1}=\frac{1+9}{2}=5;x_{2}=\frac{1-9}{2}=-4$

Второй корень не подходит. Скорость пешехода равна 5 км/ч.

Ответ: 5 км/ч - скорость пешехода.

Answer 2

Problem Analysis

We are given that a pedestrian started walking from point A to point B, which are 19 km apart. After half an hour, a tourist started walking from point B and met the pedestrian 9 km away from point B. The tourist was walking at a speed that was 1 km/h faster than the pedestrian. We need to find the speed of the pedestrian walking from point A.

Solution

Let's assume the speed of the pedestrian is x km/h. Since the tourist was walking 1 km/h faster than the pedestrian, the speed of the tourist is (x + 1) km/h.

We can use the formula distance = speed × time to calculate the time taken by each person to cover their respective distances.

The pedestrian took half an hour to cover a distance of 9 km. Therefore, the time taken by the pedestrian is 0.5 hours.

The tourist covered a distance of 9 km in the same time it took the pedestrian to cover 19 km minus 9 km (the distance between them when they met). Therefore, the time taken by the tourist is 0.5 hours.

Now, we can set up the following equation based on the distances and speeds:

Distance covered by the pedestrian = Distance covered by the tourist

9 km = (x + 1) km/h × 0.5 h

Simplifying the equation:

9 = 0.5(x + 1)

Solving for x:

18 = x + 1

x = 17

Therefore, the speed of the pedestrian walking from point A is 17 km/h.

Answer

The speed of the pedestrian walking from point A is 17 km/h.