Question

Старший брат,младший брат и сестра вместе слепили снеговика за 12 минут . Старший брат может слепить за 24 минуты , младший за 40 минут. За сколько минут может слепить снеговика сестра? (задачи на совместную работу) , знаю , что ответ 1 час , а как решить не знаю , помогите пожалуйста.

Answer 1

1/24+1/40+1/x=1/12
x-?
1/x=1/24-1/40
1/x=1/60
x=60минут

Answer 2

Problem Analysis

We are given that the older brother can build a snowman in 24 minutes, the younger brother can build a snowman in 40 minutes, and the three siblings together can build a snowman in 12 minutes. We need to determine how long it would take for the sister to build a snowman on her own.

Solution

Let's assume that the sister can build a snowman in x minutes. We can use the concept of "work done" to solve this problem. The work done by each sibling is inversely proportional to the time taken.

The work done by the older brother in 1 minute is 1/24 of the total work, as he can complete the snowman in 24 minutes.

The work done by the younger brother in 1 minute is 1/40 of the total work, as he can complete the snowman in 40 minutes.

The work done by the sister in 1 minute is 1/x of the total work, as she can complete the snowman in x minutes.

When the three siblings work together for 1 minute, they complete 1/12 of the total work, as they can complete the snowman in 12 minutes.

According to the problem, the sum of the work done by each sibling in 1 minute should be equal to the work done when they work together for 1 minute. Therefore, we can write the equation:

(1/24) + (1/40) + (1/x) = 1/12

To solve this equation for x, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 120x:

5x + 3x + 10 = 10x

Rearranging the equation, we get:

10x - 5x - 3x = 10

2x = 10

x = 10/2

x = 5

Therefore, it would take the sister 5 minutes to build a snowman on her own.

Answer

The sister can build a snowman on her own in 5 minutes.

Explanation

To solve this problem, we used the concept of "work done" and set up an equation based on the work done by each sibling in 1 minute. By solving the equation, we found that it would take the sister 5 minutes to build a snowman on her own.