Question

Помогите пожалуйста решить задачу: Винни-Пух собирается пойти навстречу своему другу Пятачку, который тоже собирается идти к нему в гости. Расстояние между их домами 840 метров. Винни-Пух идет со скоростью 42 м/мин, Пятачок – 63 м/мин. 1. Через сколько минут они встретятся, если выйдут одновременно? 2. Через сколько минут после выхода из дома Винни-Пух встретит Пятачка, если Винни-Пух выйдет на 5 минут раньше него? 3. На сколько минут раньше нужно выйти Винни-Пуху из своего дома, чтобы застать Пятачка дома?

Answer 1

1) 42+63=105 м/мин (общая скорость Пятачка и Вини)
   840 : 105= 8 мин ( время встречи если выйдут одновременно)
2) 42*5=210 м (пройдет Вини за 5 минут)
     (840-210) : 105=6 минут 
     6+5=11 минут
3) 840:42=20 минут (на 20 мин раньше Вини нужно выйти чтобы Пятачок остался дома)
  

Answer 2

Problem Analysis

To solve this problem, we need to calculate the time it takes for Winnie the Pooh and Piglet to meet each other. We are given the distance between their houses, the speeds at which they walk, and the time difference between their departures. We can use the formula `time = distance / speed` to calculate the time it takes for each scenario.

Solution

1. To find the time it takes for Winnie the Pooh and Piglet to meet if they leave their houses at the same time: - Distance between their houses: 840 meters - Winnie the Pooh's speed: 42 m/min - Piglet's speed: 63 m/min - Time taken by Winnie the Pooh to meet Piglet: 840 / (42 + 63) = 840 / 105 = 8 minutes.

2. To find the time it takes for Winnie the Pooh to meet Piglet if Winnie the Pooh leaves 5 minutes earlier: - Winnie the Pooh's departure time: 0 minutes - Piglet's departure time: 5 minutes - Winnie the Pooh's speed: 42 m/min - Piglet's speed: 63 m/min - Distance covered by Winnie the Pooh in 5 minutes: 42 * 5 = 210 meters - Remaining distance between their houses: 840 - 210 = 630 meters - Time taken by Winnie the Pooh to meet Piglet: 630 / (42 + 63) = 630 / 105 = 6 minutes.

3. To find the time Winnie the Pooh needs to leave his house earlier to catch Piglet at his house: - Winnie the Pooh's speed: 42 m/min - Piglet's speed: 63 m/min - Distance between their houses: 840 meters - Time taken by Piglet to reach Winnie the Pooh's house: 840 / 63 = 13.33 minutes - Winnie the Pooh needs to leave his house 13.33 minutes - 8 minutes = 5.33 minutes earlier to catch Piglet at his house.

Summary

Here are the answers to the given questions: 1. Winnie the Pooh and Piglet will meet if they leave their houses at the same time after 8 minutes. 2. If Winnie the Pooh leaves 5 minutes earlier, he will meet Piglet after 6 minutes. 3. Winnie the Pooh needs to leave his house 5.33 minutes earlier to catch Piglet at his house.