Question

РЕБЯТ,НУ СРОЧНО НУЖНО,ХЕЛПАНИТЕ. Мастер и ученик, работая совместно ,могут выполнить задание за 6 ч 40 мин.Если сначала будет работать только мастер и выполнит половину задания , а затем его сменит ученик и выполнит оставшуюся часть задания , то задание будет выполнено за 15 часов.За сколько часов могут выполнить задание мастер и за сколько ученик ,работая отдельно?

Answer 1

1/m+1/y=1/400 в минутах
m/2+y/2=900 в минутах

m=1800-y

400*1800=1800y-y^2
y^2-1800y+720000=0
y=900+-√(90000)=1200;600 минут
ученик за 20 часов , мастер за 10 часов

Answer 2

Task Analysis

We are given the information that a master and an apprentice can complete a task together in 6 hours and 40 minutes. If the master works alone for the first half of the task and then the apprentice takes over and completes the remaining half, the task will be completed in 15 hours. We need to determine how long it would take for the master and the apprentice to complete the task individually.

Solution

Let's assume that the master's work rate is represented by M (in terms of the fraction of the task completed per hour) and the apprentice's work rate is represented by A (in terms of the fraction of the task completed per hour).

According to the given information, when the master and the apprentice work together, they can complete the task in 6 hours and 40 minutes, which is equivalent to 6.67 hours. This can be expressed as the following equation:

6.67(M + A) = 1 (Equation 1)

We are also given that if the master works alone for the first half of the task and then the apprentice takes over and completes the remaining half, the task will be completed in 15 hours. This can be expressed as the following equation:

0.5M + 0.5A = 1 (Equation 2)

We can solve this system of equations to find the individual work rates of the master and the apprentice.

Solving the Equations

Let's solve the system of equations (Equation 1 and Equation 2) to find the values of M and A.

From Equation 2, we can express M in terms of A:

M = 2 - A (Equation 3)

Substituting Equation 3 into Equation 1, we get:

6.67((2 - A) + A) = 1

Simplifying the equation:

6.67(2) = 1

13.34 = 1

Dividing both sides by 13.34:

1 = 0.075

Therefore, the master's work rate (M) is 0.075 (or 7.5% of the task completed per hour).

Substituting this value of M into Equation 3, we can find the apprentice's work rate (A):

A = 2 - M

A = 2 - 0.075

A = 1.925

Therefore, the apprentice's work rate (A) is 1.925 (or 192.5% of the task completed per hour).

Individual Completion Times

Now that we have the individual work rates of the master and the apprentice, we can calculate how long it would take for each of them to complete the task individually.

For the master: Time taken by the master = 1 / M = 1 / 0.075 = 13.33 hours

For the apprentice: Time taken by the apprentice = 1 / A = 1 / 1.925 = 0.52 hours

Therefore, it would take the master approximately 13.33 hours and the apprentice approximately 0.52 hours to complete the task individually.

Conclusion

- The master and the apprentice, working together, can complete the task in 6 hours and 40 minutes. - The master would take approximately 13.33 hours to complete the task individually. - The apprentice would take approximately 0.52 hours to complete the task individually.

Please note that the values provided are approximate and rounded for simplicity.