2 teams consisting of workers of the same qualifications.

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Two teams, consisting of workers of the same qualifications, simultaneously began to fulfill two identical orders. The first team had `13` workers, and the second team had `23` workers. `3` days after the start of work, `20` workers from the second brigade transferred to the first brigade. As a result, both orders were completed simultaneously. Find how many days it took to complete the orders. Source: Unified State Exam 2018. Mathematics. Profile level. 20 test options. Thematic workbook. Ed. Yashchenko I.V./M.: 2018.-296 p.( problem 11(11))

Solution:

Let `x` be the productivity of each worker.

In `3` days the first team completed an amount of work equal to `13*x*3`. And the second brigade over the same three days completed a volume equal to `23*x*3`.

After the transfer of `20` workers from the second brigade, the first brigade became `13+20=33` workers, while the second brigade was left with `33-20=3` workers.

Let both teams complete the rest of the work in `t` days. Because Both orders were completed at the same time, then we can create the equation:

`13*3*x+33*x*t=23*3*x+3*x*t`;

`39x+33xt=69x+3xt`;

It turns out that after the workers moved from the second team to the first, the remaining part of the work was completed in `1` day. And taking into account the first `3` days, we get that the workers spent `3+1=4` days to complete the order.