Question

Бельчонок Вася собирает орехи с одного дерева за 50 минут, Петя – за 1 час 15 минут, а Саша – за 1 час 20 минут. С какого количества деревьев бельчата смогут собрать все орехи, работая вместе 4 часа? Они могут помогать друг другу и собирать орехи с одного дерева вместе.

Answer 1

Ответ:

11 деревьев

Пошаговое объяснение:

4×60/50+4×60/(60+20)×4×60/(60+15)=579/120+360/120+384/120=1320/120=11

Answer 2

Problem Analysis

We are given that Vasya can collect nuts from one tree in 50 minutes, Petya can collect nuts from one tree in 1 hour 15 minutes, and Sasha can collect nuts from one tree in 1 hour 20 minutes. We need to determine how many trees the squirrels can collect nuts from when working together for 4 hours.

Solution

To solve this problem, we can calculate the number of trees each squirrel can collect nuts from in 1 hour and then add up their individual rates to find the total number of trees they can collect nuts from in 4 hours.

Let's calculate the number of trees each squirrel can collect nuts from in 1 hour:

- Vasya can collect nuts from one tree in 50 minutes, which means he can collect nuts from 1/50 of a tree in 1 minute. Therefore, he can collect nuts from (1/50) * 60 = 6/5 trees in 1 hour. - Petya can collect nuts from one tree in 1 hour 15 minutes, which means he can collect nuts from 1/(1 hour 15 minutes) of a tree in 1 minute. To simplify the calculation, let's convert 1 hour 15 minutes to minutes: 1 hour 15 minutes = 60 minutes + 15 minutes = 75 minutes. Therefore, Petya can collect nuts from 1/75 of a tree in 1 minute. Therefore, he can collect nuts from (1/75) * 60 = 4/5 trees in 1 hour. - Sasha can collect nuts from one tree in 1 hour 20 minutes, which means he can collect nuts from 1/(1 hour 20 minutes) of a tree in 1 minute. To simplify the calculation, let's convert 1 hour 20 minutes to minutes: 1 hour 20 minutes = 60 minutes + 20 minutes = 80 minutes. Therefore, Sasha can collect nuts from 1/80 of a tree in 1 minute. Therefore, he can collect nuts from (1/80) * 60 = 3/4 trees in 1 hour.

Now, let's calculate the total number of trees they can collect nuts from in 4 hours by adding up their individual rates:

- Vasya can collect nuts from 6/5 trees in 1 hour. - Petya can collect nuts from 4/5 trees in 1 hour. - Sasha can collect nuts from 3/4 trees in 1 hour.

Therefore, working together for 4 hours, they can collect nuts from:

4 * (6/5 + 4/5 + 3/4) = 4 * (24/20 + 16/20 + 15/20) = 4 * (55/20) = 11 trees.

So, they can collect nuts from a total of 11 trees when working together for 4 hours.

Answer

The squirrels can collect nuts from a total of 11 trees when working together for 4 hours.