Question

После того, как к двум рабочим присоединился третий, их общая производительность возросла в два раза. Какова в процентах производительность третьего рабочего относительно производительности второго, если первый и третий рабочие за две смены выполняют тот же объём работы, что второй рабочий за пять смен?

Answer 1

Производительность первого x, второго y,  третьего z.

По условию задачи

$\frac{x+y+z}{x+y}=2\Rightarrow x+y+z=2x+2y\Rightarrow z=x+y$

Первый и третий рабочие за две смены выполнят 3(x+z), второй за пять смен 5y.

3(x+z)=5y

Из уравнения z=x+y выведем x=z-y и подставим в предыдущее уравнение:

 

$3(x+z)=5y,\quad x=z-y\\ 3(z-y+z)=5y\\ 6z-3y=5y\\ 6z=8y\\ \frac zy=\frac86=\frac43=133\frac13\%$

- производительность третьего рабочего относительно производительности второго.

Answer 2

Calculation of the Third Worker's Productivity Relative to the Second Worker

To determine the productivity of the third worker relative to the second worker, we need to compare the amount of work they each complete in a given time period.

According to the information provided, the first and third workers complete the same amount of work in two shifts, while the second worker completes the same amount of work in five shifts.

Since the total productivity of the three workers combined has doubled after the third worker joined, it means that the third worker's contribution is equal to the combined productivity of the first and second workers before the third worker joined.

Let's denote the productivity of the second worker as "x."

Before the third worker joined, the combined productivity of the first and second workers was 2x.

After the third worker joined, the combined productivity of all three workers became 4x.

To find the productivity of the third worker relative to the second worker, we can subtract the productivity of the second worker from the combined productivity of all three workers:

4x - x = 3x

Therefore, the productivity of the third worker is three times the productivity of the second worker.

In terms of percentages, the productivity of the third worker relative to the second worker can be calculated as follows:

Percentage = (Productivity of the Third Worker / Productivity of the Second Worker) * 100

Substituting the values:

Percentage = (3x / x) * 100 = 300%

Therefore, the productivity of the third worker is 300% relative to the productivity of the second worker.

Please note that the calculation assumes that the productivity of each worker remains constant over time and that there are no other factors affecting their productivity.