Question

Восьмиклассники Дима и Паша пришли на стадион заниматься бегом оказалось что Дима пробегает один круг по стадиону за t1 =1.5 мин.Если же Дима и Паша стартуя с одного места побегут по одной дорожке в разные стороны , то ои встретяться через t2=50 сек.определите время за которое Паша пробегает один круг .Считать ,что Дима и Паша бегают с постоянной скоростью

Answer 1

Переводим единицы времени.
1,5 мин = 90 сек.
Обозначим длину круга = S.
Скорость Димы = 
V1 = S/t1 = S/90
Бегут навстречу - скорости суммируются.
t2 = S/(V1 + V2) = 50
S = 50*(V1 + V2) = 5/9*S + 50*V2
4/9 * S = 50*V2
Время Паши
t3 = S/V2 = 50 : 4/9 = 450/4 = 112.5 сек = 1 мин 52,5 сек - ОТВЕТ

Answer 2

Problem Analysis

We are given that Dima and Pasha, two eighth-grade students, come to the stadium to practice running. Dima can complete one lap around the stadium in t1 = 1.5 minutes. If Dima and Pasha start from the same point and run in opposite directions on separate tracks, they will meet after t2 = 50 seconds. We need to determine the time it takes for Pasha to complete one lap around the stadium.

Solution

Let's assume that Pasha takes t minutes to complete one lap around the stadium. Since Dima and Pasha meet after t2 = 50 seconds, we can set up the following equation based on their relative speeds:

Dima's speed = Distance / Time = 1 lap / t1 minutes Pasha's speed = Distance / Time = 1 lap / t minutes

Since they meet after t2 = 50 seconds, we can write the equation:

Dima's distance = Dima's speed * t2 = 1 lap / t1 minutes * (50 seconds / 60 seconds per minute)

Similarly, Pasha's distance = Pasha's speed * t2 = 1 lap / t minutes * (50 seconds / 60 seconds per minute)

Since they are running in opposite directions, their distances should add up to one lap:

Dima's distance + Pasha's distance = 1 lap

Substituting the values, we get:

(1 lap / t1 minutes * (50 seconds / 60 seconds per minute)) + (1 lap / t minutes * (50 seconds / 60 seconds per minute)) = 1 lap

Simplifying the equation, we have:

(50 / (t1 * 60)) + (50 / (t * 60)) = 1

To find the value of t, we can solve this equation.

Calculation

Let's calculate the value of t using the given values of t1 and t2.

Substituting t1 = 1.5 minutes and t2 = 50 seconds into the equation:

(50 / (1.5 * 60)) + (50 / (t * 60)) = 1

Simplifying the equation further:

(50 / 90) + (50 / (t * 60)) = 1

Multiplying both sides of the equation by 90t:

50t + 50 * 90 = 90t

Simplifying the equation:

50 * 90 = 90t - 50t

4500 = 40t

Dividing both sides of the equation by 40:

t = 4500 / 40

t = 112.5 seconds

Therefore, it takes Pasha 112.5 seconds to complete one lap around the stadium.

Answer

Pasha takes 112.5 seconds to complete one lap around the stadium.

Source:

'1.2. 1 1.1.2 - '