Question

Девять рабочих, работая с одинаковой производительностью,могут выполнить работу за 10 часов. Сколько ещё нужно рабочих,чтобы эта работа была выполнена за 6 часов!?Помогайте... Ответ должен быть 6!! Но не могу найти решение

Answer 1

10*9х = 6x(9+N)
       
90 = 54 + 6N    
6N=90-54     
6N = 36
N=6
x-производительность 1-го рабочего
N- число приглашенных рабочих

Answer 2

Calculating the Number of Workers Needed to Complete a Task

To determine the number of additional workers needed to complete a task in a shorter time frame, we can use the concept of work rate. The work rate is the amount of work done per unit of time by an individual worker.

Given that nine workers, each with the same productivity, can complete the task in 10 hours, we can calculate the total work required to complete the task. Let's assume that the total work is represented by W.

The work rate of each worker can be calculated by dividing the total work by the number of workers and the time taken to complete the task. In this case, the work rate is given by:

Work rate = W / (9 * 10)

To complete the task in 6 hours, we need to calculate the work rate required to achieve this time frame. Let's assume that the number of additional workers needed is represented by x.

The work rate required to complete the task in 6 hours is given by:

Work rate = W / ((9 + x) * 6)

Since the work rate remains constant, we can equate the two expressions for the work rate:

W / (9 * 10) = W / ((9 + x) * 6)

To solve for x, we can cross-multiply and simplify the equation:

W * (9 + x) * 6 = W * 9 * 10

Cancelling out the W terms, we get:

(9 + x) * 6 = 9 * 10

Simplifying further:

54 + 6x = 90

Subtracting 54 from both sides:

6x = 36

Dividing both sides by 6:

x = 6

Therefore, to complete the task in 6 hours, we would need an additional 6 workers.

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