Question

Витя может выполнить некоторую работу за 9 часов, Саша может выполнить эту же работу за 12 часов, а Вова - за 18 часов. За сколько часов смогут выполнить работу ребята, если будут работать вместе?

Answer 1

Ответ:

13часов

Пошаговое объяснение:

насколько я понял нужно среднее арефметическое

(9+12+18):3

Answer 2

Problem Analysis

We are given that Vitya can complete a certain task in 9 hours, Sasha can complete the same task in 12 hours, and Vova can complete it in 18 hours. We need to determine how long it will take for them to complete the task if they work together.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. If we let x represent the number of hours it takes for the three of them to complete the task together, we can set up the following equation:

Vitya's work rate + Sasha's work rate + Vova's work rate = Combined work rate

The work rate is inversely proportional to the time taken to complete the task. Therefore, the work rate is equal to 1 divided by the time taken. Using this information, we can set up the equation as follows:

1/9 + 1/12 + 1/18 = 1/x

To solve for x, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 36:

4/36 + 3/36 + 2/36 = 1/x

Simplifying the equation, we get:

9/36 = 1/x

Cross-multiplying, we have:

9x = 36

Dividing both sides of the equation by 9, we find:

x = 4

Therefore, it will take the three of them 4 hours to complete the task if they work together.

Answer

If Vitya can complete the task in 9 hours, Sasha can complete it in 12 hours, and Vova can complete it in 18 hours, then it will take them 4 hours to complete the task if they work together.