Question

Две бригады состоящие из рабочих одинаковой квалификации одновременно начали строить два одинаковых летних домика. 1ой бригаде было 7 рабочих а во второй 13 рабочих через 8 дней после начала работы в первую бригаду перешли 7 рабочих из 2ой бригады в результате чего оба домика были построены одновременно. сколько дней потребовалось бригадам чтобы закончить работу в новом составе?

Answer 1

Х скорость одного рабочего в день
т.е. первая бригада делала в день 7х
вторая 13 х
за 8 дней первая сдлелал 7х*8=56х  вторая 13х*8=104х
дальше перешло 7 человек 
первая бригада работала со скоростью 14х а вторая 6х
вторая к тому моменту опережала первую на 104х-56х=48х
в день первая сокращала разрыв на 14х-6х=8х
и сократила его за 48х/8х=6 дней


проверка

7х*8+14х*6=13х*8+6х*6
56х+84х=104х+36х
140х=140х

Answer 2

Problem Analysis

We have two brigades, each consisting of workers of the same qualification, simultaneously building two identical summer houses. The first brigade has 7 workers, and the second brigade has 13 workers. After 8 days of work, 7 workers from the second brigade joined the first brigade, resulting in both houses being completed simultaneously. We need to determine how many days it took for the brigades to finish the work in the new composition.

Solution

To solve this problem, we can use the concept of "worker-days." A worker-day represents the work done by one worker in one day. We can calculate the total worker-days required to complete the houses for each brigade and then determine the number of days it took for both houses to be completed simultaneously.

Let's calculate the worker-days for each brigade:

- The first brigade has 7 workers, and they worked for 8 days. So, the total worker-days for the first brigade is 7 * 8 = 56 worker-days. - The second brigade has 13 workers, and they also worked for 8 days. So, the total worker-days for the second brigade is 13 * 8 = 104 worker-days.

Since both houses were completed simultaneously, the total worker-days for both brigades must be equal. Let's assume it took x days for both houses to be completed in the new composition.

- The first brigade worked for x days with 7 workers, so the total worker-days for the first brigade in the new composition is 7 * x = 7x worker-days. - The second brigade worked for (8 - x) days with 6 workers (13 - 7 workers who joined the first brigade), so the total worker-days for the second brigade in the new composition is 6 * (8 - x) = 48 - 6x worker-days.

Since both houses were completed simultaneously, the total worker-days for both brigades must be equal:

7x = 48 - 6x

Let's solve this equation to find the value of x:

7x + 6x = 48

13x = 48

x = 48 / 13

x ≈ 3.6923

Therefore, it took approximately 3.6923 days for both brigades to finish the work in the new composition.

Answer

It took approximately 3.6923 days for both brigades to finish the work in the new composition.