Question

Из пункта А в направлении пункта В выехал велосипедист со скоростью 5 м/с. Одновременно с ним в том же направлении из пункта В вышел пешеход. Через некоторое время велосипедист догнал пешехода на расстоянии от пункта В, в 3 раза меньшем, чем расстояние от А до В. С какой скоростью (км/ч) двигался пешеход?

Answer 1

5 м/с=5*3600/1000=18 км/ч

Пусть х км/ч - скорость пешехода, t ч. - время до встречи. За это время велосипедист преодолел расстояние 18t км, а пешеход хt км. Расстояние от А до В равно 3хt км или 18t-xt. Составим и решим уравнение:

3хt=18t-xt

3xt+xt=18t

4xt=18t

x=18t:4t

x=4,5

Ответ: пешеход двигался со скоростью 4,5 км/ч.

Answer 2

Problem Analysis

We are given that a cyclist travels from point A to point B at a speed of 5 m/s, while a pedestrian simultaneously walks in the same direction from point B. After some time, the cyclist catches up to the pedestrian at a distance from point B that is three times smaller than the distance from point A to point B. We need to determine the speed at which the pedestrian is moving.

Solution

Let's assume that the distance from point A to point B is represented by x. According to the problem statement, the cyclist catches up to the pedestrian at a distance from point B that is three times smaller than x. Therefore, the distance from the cyclist to point B is x/3.

We know that the cyclist's speed is 5 m/s. Let's denote the time it takes for the cyclist to catch up to the pedestrian as t. During this time, the cyclist travels a distance of 5t.

Since the cyclist catches up to the pedestrian at a distance of x/3 from point B, we can write the equation:

5t = x - x/3

Simplifying the equation, we get:

5t = 2x/3

Now, let's consider the pedestrian's speed. The pedestrian is moving at a speed that we need to determine. Let's denote the pedestrian's speed as v. During the time t, the pedestrian travels a distance of vt.

Since the pedestrian is caught by the cyclist at a distance of x/3 from point B, we can write the equation:

vt = x/3

Simplifying the equation, we get:

v = x/3t

To find the speed of the pedestrian in km/h, we need to convert the units. 1 m/s is equal to 3.6 km/h. Therefore, the speed of the pedestrian in km/h is:

v (km/h) = (x/3t) * 3.6

Now, let's substitute the value of t from the equation 5t = 2x/3 into the equation for v:

v (km/h) = (x/3(2x/15)) * 3.6

Simplifying the equation, we get:

v (km/h) = (5x/2x) * 3.6

Simplifying further, we get:

v (km/h) = 9 km/h

Therefore, the pedestrian is moving at a speed of 9 km/h.

Answer

The pedestrian is moving at a speed of 9 km/h.