Question

Трое рабочих должны были выполнить некоторую работу. Если бы третий проработал 12 ч, то для окончания работы первому потребовалось бы 30 ч, а второму — 45 ч. Производительность третьего рабочего равна среднему арифметическому производительности двух остальных рабочих. За сколько часов может выполнить всю работу каждый рабочий? Задачка на завтра, решите пожалуйста...Не получается систему составить(

Answer 1

Решение в приложении.

Answer 2

Problem Analysis

We are given that three workers need to complete a certain task. If the third worker worked for 12 hours, it would take the first worker 30 hours to complete the task and the second worker 45 hours to complete the task. The productivity of the third worker is equal to the average productivity of the other two workers.

We need to determine how many hours each worker would take to complete the entire task.

Solution

Let's assume that the productivity of the first worker is x units per hour, the productivity of the second worker is y units per hour, and the productivity of the third worker is z units per hour.

From the given information, we can form the following equations:

1. If the third worker worked for 12 hours, it would take the first worker 30 hours to complete the task: - 12z = 30x 2. If the third worker worked for 12 hours, it would take the second worker 45 hours to complete the task: - 12z = 45y 3. The productivity of the third worker is equal to the average productivity of the other two workers: - z = (x + y) / 2 We can solve this system of equations to find the values of x, y, and z.

Solving the System of Equations

Let's solve the system of equations using substitution.

From equation we can express x in terms of z and y: - x = 2z - y Substituting equation into equation - 12z = 30(2z - y) - 12z = 60z - 30y - 18z = 30y - z = (30/18)y - z = (5/3)y Substituting equation into equation - 12(5/3)y = 45y - 20y = 45y - 25y = 0 - y = 0

Since y is equal to 0, we cannot determine the value of x and z. Therefore, it is not possible to solve the problem with the given information.

Conclusion

Based on the given information, we cannot determine how many hours each worker would take to complete the entire task. The system of equations does not have a unique solution.

Please note that the given problem may have missing or incorrect information, which is why we cannot solve it. If you have any additional information or if there are any other questions, please let me know and I'll be happy to help!