Question

Школьники занимаются прополкой огорода, который находится на пришкольном участке. Работают они с разной скоростью, а некоторые из них, как показывает практика, даже мешают общей работе, просто закапывая сорняки или перебрасывая их на участок соседа... Вчерашняя работа показала, что Вася и Алина выпалывают гряду за 14 мин, Алина и Николай выпалывают её же за 28 мин, Николай и Вася — за 56 мин. - За сколько минут выполнят эту работу все Вместе? Ответ: Втроём дети выполнят работу за ​

Answer 1

Ответ:

16

Объяснение:

За единицу примем работу.

1/14=4/56 - производительность Васи и Алины.

1/28=2/56 - производительность Алины и Николая.

1/56 - производительность Николая и Васи.

Чтобы посчитать производительность всех троих, необходимо исключить дублирование, значит, делим на два:

(4/56 +2/56 +1/56)/2=7/112 - производительность всех троих.

Посчитаем за сколько минут выполнят эту работу все вместе:

1/(7/112)=112/7=16 мин

Answer 2

Problem Analysis

The problem states that a group of students is weeding a garden on the school grounds. Each student works at a different speed, and some of them even hinder the overall progress by burying weeds or throwing them onto a neighbor's plot. The problem provides information about the time it takes for different pairs of students to weed a specific row. We need to determine how long it will take for all three students to complete the task together.

Solution

To solve this problem, we can use the concept of "work rates." The work rate of a person is the amount of work they can complete in a given time. If we know the work rates of two people, we can calculate the time it takes for them to complete a task together.

Let's assign variables to the work rates of each student: - Vasya's work rate: V - Alina's work rate: A - Nikolay's work rate: N

From the given information, we know the following: - Vasya and Alina can weed the row in 14 minutes. - Alina and Nikolay can weed the same row in 28 minutes. - Nikolay and Vasya can weed the same row in 56 minutes.

Using the concept of work rates, we can set up the following equations:

1. Vasya and Alina's combined work rate: (V + A) - They can complete the task in 14 minutes. - Therefore, their combined work rate is 1/14 of the task per minute.

2. Alina and Nikolay's combined work rate: (A + N) - They can complete the task in 28 minutes. - Therefore, their combined work rate is 1/28 of the task per minute.

3. Nikolay and Vasya's combined work rate: (N + V) - They can complete the task in 56 minutes. - Therefore, their combined work rate is 1/56 of the task per minute.

Now, we need to find the combined work rate of all three students working together. Let's call it (V + A + N).

To find the combined work rate of all three students, we can add up the individual work rates of each pair of students and subtract the work rate of the remaining student. This can be represented by the equation:

(V + A + N) = (V + A) + (A + N) + (N + V) - V - A - N

Simplifying the equation, we get:

(V + A + N) = 1/14 + 1/28 + 1/56

Now, we can calculate the combined work rate of all three students.

Calculation

Let's calculate the combined work rate of all three students:

(V + A + N) = 1/14 + 1/28 + 1/56

Using a common denominator of 56, we get:

(V + A + N) = 4/56 + 2/56 + 1/56

Combining the fractions, we get:

(V + A + N) = 7/56

Simplifying the fraction, we get:

(V + A + N) = 1/8

This means that all three students together can complete 1/8 of the task per minute.

Final Answer

To find the time it takes for all three students to complete the task together, we need to calculate the reciprocal of their combined work rate:

Time = 1 / (V + A + N)

Substituting the value of (V + A + N), we get:

Time = 1 / (1/8)

Simplifying the expression, we get:

Time = 8 minutes

Therefore, all three students will complete the task together in 8 minutes.

Answer

The three students will complete the weeding task together in 8 minutes.