Question

Два пешехода вышли одновременно из пункта А.. Первый из них встретился с туристом, идущим в А. через 20 мин после выхода из А, а второй встретил туриста на 5 мин позже первого. Через 10 мин после второй встречи турист пришел в А. Скорости пешеходов и туриста постоянны. Найдите отношение скоростей пешеходов.​

Answer 1

Ответ:

Скорость первого пешехода в 1,5 (полтора раза) больше скорости второго.

Пошаговое объяснение:

пусть скорость V₁, V₂, Vт скорость 1-ого пешехода, 2-ого пешехода и туриста соответственно.

Тогда можем записать, что скорость второго пешехода равна:

V₂=S₂/(20+5)=S₂/25, где

S₂ - расстояние от пункта А до места встречи второго пешехода с туристом. Очевидно, что скорость туриса равна:

Vт=S₂/10 (он это расстояние "пробежал" за 10 мин).

Отношение скоростей второго пешехода и туриста:

V₂/Vт=(S₂/25)/(S₂/10)=10/25=2/5.

V₂=Vт*2/5

Возьмемся за первого пешехода.

Скорость первого пешехода равна:

V₁=S₁/20, где

S₁ - расстояние от пункта А до места встречи первого пешехода с туристом. Очевидно, что скорость туриса равна:

Vт=S₁/(5+10)=S₁/15 (через 5 мин турист встретиля со вторым пешеходом, и через 10 мин турист добежал до пункта А).

Отношение скоростей первого пешехода и туриста:

V₁/Vт=(S₁/20)/(S₁/15)=15/25=3/5.

V₁=Vт*3/5

Т.к. по условию скорости всех людей на всем пути постоянны, то можем смело записать:

V₁/V₂=(Vт*3/5)/(Vт*2/5)=3/2=1,5.

Скорость первого пешехода в полтора раза больше скорости второго.

Answer 2

Problem Analysis

We are given that two pedestrians leave point A simultaneously. The first pedestrian meets a tourist who is walking towards point A 20 minutes after leaving point A. The second pedestrian meets the tourist 5 minutes after the first pedestrian. After the second meeting, the tourist arrives at point A 10 minutes later. We need to find the ratio of the speeds of the pedestrians.

Solution

Let's assume the speed of the first pedestrian is v1 and the speed of the second pedestrian is v2. The speed of the tourist will be denoted as vt.

We can start by calculating the time it takes for the first pedestrian to meet the tourist. Since the tourist is walking towards point A, the relative speed between the first pedestrian and the tourist will be the sum of their speeds: v1 + vt. The time it takes for them to meet is given as 20 minutes.

Similarly, the time it takes for the second pedestrian to meet the tourist can be calculated as the relative distance divided by the relative speed: 5 / (v2 + vt).

Finally, we know that after the second meeting, the tourist arrives at point A 10 minutes later. This means that the time it takes for the tourist to reach point A from the second meeting point is 10 minutes. We can calculate this time as the distance divided by the tourist's speed: 10 / vt.

Now, we can set up the following equations:

Equation 1: 20 = (v1 + vt) * t1 (where t1 is the time for the first meeting) Equation 2: 5 = (v2 + vt) * t2 (where t2 is the time for the second meeting) Equation 3: 10 = 10 / vt (where 10 is the time for the tourist to reach point A)

We can solve these equations to find the ratio of the speeds of the pedestrians.

Calculation

Let's solve the equations to find the ratio of the speeds of the pedestrians.

From Equation 3, we can see that vt = 1.

Substituting this value into Equations 1 and 2, we get:

Equation 1: 20 = (v1 + 1) * t1 Equation 2: 5 = (v2 + 1) * t2

Now, let's solve these equations simultaneously.

From Equation 1, we can express t1 in terms of v1: t1 = 20 / (v1 + 1)

Substituting this value into Equation 2, we get: 5 = (v2 + 1) * (20 / (v1 + 1))

Simplifying this equation, we have: 5(v1 + 1) = 20(v2 + 1) 5v1 + 5 = 20v2 + 20

Rearranging the equation, we get: 5v1 - 20v2 = 15

Now, we can find the ratio of the speeds of the pedestrians by dividing the coefficients of v1 and v2: v1 / v2 = 15 / 5 = 3

Therefore, the ratio of the speeds of the pedestrians is 3.

Answer

The ratio of the speeds of the pedestrians is 3.