Question

Производительность мастера в 5 раз выше производительности ученика. Сколько дней потребуется для выполнения задания ученику, если известно, что при одновременной работе мастера и ученика это задание они выполнят за 3 дня?

Answer 1

Пусть 1 - весь объем работы
тогда 1/(х+у)=3
где х - скорость ввполнения ученика
а у - скорость мастера
тогда же выходит что у/х=5
тогда у=5х
теперь решаем первое уравнение
3х+3у=1
подставим вместо у 5х и получим
3х+15х=1
18х=1
х=1/18
чтобы найти время надо объем разделить на скорость
1/1/18=18дней
ответ: 18дней

Answer 2

Calculating Time Needed for Task Completion

To calculate the time needed for the apprentice to complete the task, given that the master's productivity is 5 times higher, and they can complete the task together in 3 days, we can use the following approach:

Let's assume the master's productivity is represented by M and the apprentice's productivity is represented by A. Given that the master's productivity is 5 times higher than the apprentice's productivity, we can express this relationship as:

M = 5A

When working together, their combined productivity is the sum of their individual productivities:

M + A = 1/3 (as they can complete the task in 3 days)

Using these equations, we can solve for the apprentice's productivity and then calculate the time needed for the apprentice to complete the task alone.

Solution

First, we can express the master's productivity in terms of the apprentice's productivity using the given relationship:

M = 5A Substituting this into the combined productivity equation:

5A + A = 1/3

Solving for A:

6A = 1/3

A = 1/18

Now that we have the apprentice's productivity, we can calculate the time needed for the apprentice to complete the task alone. Since the master's productivity is 5 times higher, the time needed for the apprentice to complete the task alone can be calculated using the formula:

Time = 1 / Apprentice's productivity

Substituting the value of the apprentice's productivity:

Time = 1 / (1/18)

Time = 18 days

Therefore, it will take the apprentice 18 days to complete the task alone.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.