Question

Работа выполняется первым рабочим в одиночку за а дней, второй рабочий выполня-ет работу на в дней дольше, а третий рабочий - на в дней быстрее. За сколько дней трое рабочих выполнят работу вместе?

Answer 1

Problem Analysis

We have three workers who are working on a task. The first worker completes the task in a days, the second worker takes b days longer than the first worker, and the third worker takes c days less than the first worker. We need to find out how many days it will take for all three workers to complete the task together.

Solution

Let's assume that the first worker takes x days to complete the task. According to the problem, the second worker takes b days longer than the first worker, so the second worker will take x + b days. Similarly, the third worker takes c days less than the first worker, so the third worker will take x - c days.

To find out how many days it will take for all three workers to complete the task together, we need to calculate the harmonic mean of the three times taken by each worker. The harmonic mean is given by the formula:

Harmonic Mean = 3 / ((1/x) + (1/(x+b)) + (1/(x-c)))

Let's substitute the values and calculate the result.

Calculation

Given: - First worker takes x days - Second worker takes b days longer than the first worker, so (x + b) days - Third worker takes c days less than the first worker, so (x - c) days

Using the formula for the harmonic mean, we have:

Harmonic Mean = 3 / ((1/x) + (1/(x+b)) + (1/(x-c)))

Substituting the values, we get:

Harmonic Mean = 3 / ((1/x) + (1/(x+b)) + (1/(x-c)))

Now we can calculate the result.

Answer

The three workers will complete the task together in (result) days.

Please note that due to the lack of specific values for x, b, and c in the user's question, we are unable to provide an exact answer. However, you can use the provided formula and substitute the appropriate values to calculate the result.