Question

Мастер и ученик,работая вместе ,могут выполнить всю работу за 3часа,а один мастер сделает её за 4часа. Сколько времени затратить на эту же работу только один ученик?

Answer 1

3(1/4+1/х)=1
3х+12=4х
4х-3х=12
х=12
ответ - 12 часов

Answer 2

Calculation of Time Required

To determine how much time it would take for a single apprentice to complete the same task, we can use the concept of work rates. Let's assume that the master's work rate is represented by M (in units of work per hour) and the apprentice's work rate is represented by A (in units of work per hour).

According to the given information, when the master and apprentice work together, they can complete the entire task in 3 hours. This means that their combined work rate is equal to the total amount of work divided by the time taken:

M + A = Total Work / Time

Similarly, when the master works alone, he can complete the task in 4 hours. Therefore, his work rate is:

M = Total Work / Time

By substituting the value of M from the second equation into the first equation, we can solve for A:

(Total Work / Time) + A = Total Work / 3

Simplifying the equation, we get:

A = (2 * Total Work) / 3Time

Now, we can use this equation to calculate the time required for the apprentice to complete the task alone.

Calculation of Time Required for the Apprentice

Let's assume that the total work required for the task is represented by W (in units of work). We can use the equation derived earlier to calculate the time required for the apprentice to complete the task alone:

A = (2W) / 3Time

Since we know that the master can complete the task in 4 hours, we can substitute the values into the equation:

A = (2W) / 3(4)

Simplifying the equation, we get:

A = (2W) / 12

Therefore, the time required for the apprentice to complete the task alone is (2W) / 12 hours.

Answer

Based on the given information, the master and apprentice can complete the entire task in 3 hours when working together, and the master can complete the task alone in 4 hours. Therefore, the time required for the apprentice to complete the same task alone is (2W) / 12 hours.

Please note that the specific value of W (total work) was not provided in the question, so we cannot calculate the exact time required for the apprentice.