Question

Одна бригада может убрать все поле за 12 дней.Другой бригаде для выполнения той же работы нужно 3/4 этого времени. После того как, в течении 5 дней работала только первая бригада, к ней присоединилась вторая, и обе вместе закончили работу. Сколько дней работали бригады вместе?

Answer 1

Первой бригаде для выполнения задания нужно 12 дней, а второй 9 дней, поэтому дневная производительность первой бригады равна 1/12 , второй

1/9 , а их общая дневная производительность составляет  1/12 + 1/9 = 7/36

Первая бригада, отработав 5 дней, выполнила 5/12 работы. Соответственно осталось выполнить  7/12 .

Таким образом, две бригады вместе должны работать  

(7/12) / (7/36) = 3 дня.

 

Answer 2

12:4·3=9 (дн.)-выполнит работу вторая бригада

Производительность первой бригады равна 1/12, второй - 1/9.

Пусть бригады вместе работали х дней. За это время первая бригада сделала х/12, вторая - х/9 работы. Составляем уравнение:

5/12 + х/12 + х/9 = 1

15+3х+4х=36

3х+4х=36-15

7х=21

х=3

Ответ. 3 дня. 

Answer 3

Problem Analysis

We are given that one brigade can complete a field in 12 days, while another brigade takes 3/4 of that time to complete the same work. After working alone for 5 days, the first brigade is joined by the second brigade, and together they finish the work. We need to determine how many days the brigades worked together.

Solution

Let's break down the problem step by step:

1. The first brigade can complete the field in 12 days, so their daily work rate is 1/12 of the field per day. 2. The second brigade takes 3/4 of the time, so their daily work rate is 1/(12 * 3/4) = 4/9 of the field per day. 3. After working alone for 5 days, the first brigade has completed 5 * (1/12) = 5/12 of the field. 4. When the second brigade joins, the combined work rate of both brigades is (1/12) + (4/9) = 23/36 of the field per day. 5. Let's assume the number of days the brigades work together is x. In those x days, the combined work of both brigades is x * (23/36) of the field. 6. The total work completed is the sum of the work done by the first brigade alone (5/12) and the work done by both brigades together (x * 23/36). This should equal the entire field, which is 1. 7. We can set up the equation: 5/12 + (x * 23/36) = 1. 8. Solving this equation will give us the value of x, which represents the number of days the brigades worked together.

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

5/12 + (x * 23/36) = 1

To simplify the equation, we can multiply both sides by 36:

36 * (5/12) + 36 * (x * 23/36) = 36 * 1

15 + 23x = 36

23x = 36 - 15

23x = 21

x = 21/23

Therefore, the brigades worked together for 21/23 of a day.

Answer

The brigades worked together for 21/23 of a day.