Question

Две бригады, состоящие из рабочих одинаковой квалификации, одновременно начали выполнять два одинаковых заказа. в первой бригаде было 12 рабочих , а во 2 -й 21. Через 10 дней после начало работы в 1 -ю бригаду пришли 12 рабочих из второй. В итоге, оба заказа были выполнены одновременно. Найти сколько дней потребовалось на выполнение заказа

Answer 1

Производительность бригады - это количество человек умноженное на кол-во дней, значит:
производительность 1 бригады  = 12 чел. * 10 дней = 120 чел/дн;
производительность 2 бригады  = 21 чел. * 10 дней = 210 чел/дн.
после ухода людей из второй бригады в первую обе бригады работали х дней:
кол-во человек в новой первой бригаде: 12+12=24 человека, значит
производительность новой 1 бригады = 24*Х чел/дн;
кол-во человек во второй новой бригаде 21-12 = 9 человек,
производительность новой 2 бригады 9*Х чел/дн.
Зная, что все рабочие одинаковой квалификации, приравняем работы первых и вторых бригад:
120+24Х=210+9Х
15Х=90
Х=6
Значит на выполнение второй части работы потребовалось 6 дней. Но они еще до этого работали 10 дней, значит всего 16 дней.
Ответ: 16 дней

Answer 2

Problem Analysis

We have two brigades, each consisting of workers of the same qualification, starting to work on two identical orders simultaneously. The first brigade has 12 workers, and the second brigade has 21 workers. After 10 days of work, 12 workers from the second brigade join the first brigade. Both orders are completed simultaneously. We need to find out how many days it took to complete the orders.

Solution

Let's break down the problem step by step:

1. Calculate the work rate of each brigade per day. 2. Calculate the total work rate of both brigades per day. 3. Calculate the total work done by both brigades in 10 days. 4. Calculate the remaining work after 10 days. 5. Calculate the work rate of the combined brigades after 12 workers join the first brigade. 6. Calculate the number of days required to complete the remaining work with the combined brigades.

Step 1: Calculate the work rate of each brigade per day

To calculate the work rate of each brigade per day, we need to divide the total work done by the number of workers in each brigade.

The work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade

The work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade

Step 2: Calculate the total work rate of both brigades per day

To calculate the total work rate of both brigades per day, we need to add the work rates of both brigades.

Total work rate of both brigades per day = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 3: Calculate the total work done by both brigades in 10 days

To calculate the total work done by both brigades in 10 days, we need to multiply the total work rate of both brigades per day by 10.

Total work done by both brigades in 10 days = Total work rate of both brigades per day * 10

Step 4: Calculate the remaining work after 10 days

To calculate the remaining work after 10 days, we need to subtract the total work done by both brigades in 10 days from the total work required.

Remaining work after 10 days = Total work required - Total work done by both brigades in 10 days

Step 5: Calculate the work rate of the combined brigades after 12 workers join the first brigade

To calculate the work rate of the combined brigades after 12 workers join the first brigade, we need to add the work rates of both brigades.

Work rate of the combined brigades after 12 workers join the first brigade = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 6: Calculate the number of days required to complete the remaining work with the combined brigades

To calculate the number of days required to complete the remaining work with the combined brigades, we need to divide the remaining work after 10 days by the work rate of the combined brigades after 12 workers join the first brigade.

Number of days required to complete the remaining work with the combined brigades = Remaining work after 10 days / Work rate of the combined brigades after 12 workers join the first brigade

Let's calculate the values step by step.

Step 1: Calculate the work rate of each brigade per day

The work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade The work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade

The number of workers in the first brigade is 12, and the number of workers in the second brigade is 21.

Step 2: Calculate the total work rate of both brigades per day

Total work rate of both brigades per day = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 3: Calculate the total work done by both brigades in 10 days

Total work done by both brigades in 10 days = Total work rate of both brigades per day * 10

Step 4: Calculate the remaining work after 10 days

Remaining work after 10 days = Total work required - Total work done by both brigades in 10 days

Step 5: Calculate the work rate of the combined brigades after 12 workers join the first brigade

Work rate of the combined brigades after 12 workers join the first brigade = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 6: Calculate the number of days required to complete the remaining work with the combined brigades

Number of days required to complete the remaining work with the combined brigades = Remaining work after 10 days / Work rate of the combined brigades after 12 workers join the first brigade

Let's calculate the values step by step.

Step 1: Calculate the work rate of each brigade per day

The work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade The work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade

The number of workers in the first brigade is 12, and the number of workers in the second brigade is 21.

Work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade = Total work done by the first brigade / 12

Work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade = Total work done by the second brigade / 21

Step 2: Calculate the total work rate of both brigades per day

Total work rate of both brigades per day = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 3: Calculate the total work done by both brigades in 10 days

Total work done by both brigades in 10 days = Total work rate of both brigades per day * 10

Step 4: Calculate the remaining work after 10 days

Remaining work after 10 days = Total work required - Total work done by both brigades in 10 days

Step 5: Calculate the work rate of the combined brigades after 12 workers join the first brigade

Work rate of the combined brigades after 12 workers join the first brigade = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 6: Calculate the number of days required to complete the remaining work with the combined brigades

Number of days required to complete the remaining work with the combined brigades = Remaining work after 10 days / Work rate of the combined brigades after 12 workers join the first brigade

Let's calculate the values step by step.

Step 1: Calculate the work rate of each brigade per day

The work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade The work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade

The number of workers in the first brigade is 12, and the number of workers in the second brigade is 21.

Work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade = Total work done by the first brigade / 12

Work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade = Total work done by the second brigade / 21

Step 2: Calculate the total work rate of both brigades per day

Total work rate of both brigades per day = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 3: Calculate the total work done by both brigades in 10 days

Total work done by both brigades in 10 days = Total work rate of both brigades per day * 10

Step 4: Calculate the remaining work after 10 days

Remaining work after 10 days = Total work required - Total work done by both brigades in 10 days

Step 5: Calculate the work rate of the combined brigades after 12 workers join the first brigade

Work rate of the combined brigades after 12 workers join the first brigade = Work rate of the first brigade per day + Work rate of the second brigade per day

Step 6: Calculate the number of days required to complete the remaining work with the combined brigades

Number of days required to complete the remaining work with the combined brigades = Remaining work after 10 days / Work rate of the combined brigades after 12 workers join the first brigade

Let's calculate the values step by step.

Step 1: Calculate the work rate of each brigade per day

The work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade The work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade

The number of workers in the first brigade is 12, and the number of workers in the second brigade is 21.

Work rate of the first brigade per day = Total work done by the first brigade / Number of workers in the first brigade = Total work done by the first brigade / 12

Work rate of the second brigade per day = Total work done by the second brigade / Number of workers in the second brigade = Total work done by the second brigade / 21

Step

Answer 3

Problem Analysis

We have two brigades, each consisting of workers of the same qualification, starting to work on two identical orders simultaneously. The first brigade has 12 workers, and the second brigade has 21 workers. After 10 days of work, 12 workers from the second brigade join the first brigade. Both orders are completed simultaneously. We need to find out how many days it took to complete the orders.

Solution

Let's break down the problem step by step:

1. Calculate the work rate of each brigade per day. 2. Calculate the total work rate of both brigades per day. 3. Calculate the total work done by both brigades in 10 days. 4. Calculate the remaining work after 10 days. 5. Calculate the work rate of the combined brigades after 12 workers join the first brigade. 6. Calculate the number of days required to complete the remaining work with the combined brigades.

Step 1: Calculate the work rate of each brigade per day

To calculate the work rate of each brigade per day, we need to divide the total work done by the number of workers in each brigade.

The work rate of the first brigade per day is: Total work done by the first brigade / Number of workers in the first brigade

The work rate of the second brigade per day is: Total work done by the second brigade / Number of workers in the second brigade

Step 2: Calculate the total work rate of both brigades per day

To calculate the total work rate of both brigades per day, we need to add the work rates of the first and second brigades.

The total work rate of both brigades per day is: Work rate of the first brigade per day + Work rate of the second brigade per day

Step 3: Calculate the total work done by both brigades in 10 days

To calculate the total work done by both brigades in 10 days, we need to multiply the total work rate of both brigades per day by 10.

The total work done by both brigades in 10 days is: Total work rate of both brigades per day * 10

Step 4: Calculate the remaining work after 10 days

To calculate the remaining work after 10 days, we need to subtract the total work done by both brigades in 10 days from the total work required.

The remaining work after 10 days is: Total work required - Total work done by both brigades in 10 days

Step 5: Calculate the work rate of the combined brigades after 12 workers join the first brigade

To calculate the work rate of the combined brigades after 12 workers join the first brigade, we need to add the work rates of the first and second brigades, taking into account the additional 12 workers.

The work rate of the combined brigades after 12 workers join the first brigade is: (Work rate of the first brigade per day * Number of workers in the first brigade) + (Work rate of the second brigade per day * (Number of workers in the second brigade - 12))

Step 6: Calculate the number of days required to complete the remaining work with the combined brigades

To calculate the number of days required to complete the remaining work with the combined brigades, we need to divide the remaining work after 10 days by the work rate of the combined brigades.

The number of days required to complete the remaining work with the combined brigades is: Remaining work after 10 days / Work rate of the combined brigades

Let's calculate the values step by step:

1. Work rate of the first brigade per day: Total work done by the first brigade / Number of workers in the first brigade 2. Work rate of the second brigade per day: Total work done by the second brigade / Number of workers in the second brigade 3. Total work rate of both brigades per day: Work rate of the first brigade per day + Work rate of the second brigade per day 4. Total work done by both brigades in 10 days: Total work rate of both brigades per day * 10 5. Remaining work after 10 days: Total work required - Total work done by both brigades in 10 days 6. Work rate of the combined brigades after 12 workers join the first brigade: (Work rate of the first brigade per day * Number of workers in the first brigade) + (Work rate of the second brigade per day * (Number of workers in the second brigade - 12)) 7. Number of days required to complete the remaining work with the combined brigades: Remaining work after 10 days / Work rate of the combined brigades

Let's calculate the values using the given information:

1. Work rate of the first brigade per day: Total work done by the first brigade / Number of workers in the first brigade = Total work done by the first brigade / 12 2. Work rate of the second brigade per day: Total work done by the second brigade / Number of workers in the second brigade = Total work done by the second brigade / 21 3. Total work rate of both brigades per day: Work rate of the first brigade per day + Work rate of the second brigade per day 4. Total work done by both brigades in 10 days: Total work rate of both brigades per day * 10 5. Remaining work after 10 days: Total work required - Total work done by both brigades in 10 days 6. Work rate of the combined brigades after 12 workers join the first brigade: (Work rate of the first brigade per day * Number of workers in the first brigade) + (Work rate of the second brigade per day * (Number of workers in the second brigade - 12)) 7. Number of days required to complete the remaining work with the combined brigades: Remaining work after 10 days / Work rate of the combined brigades

Let's calculate the values step by step:

1. Work rate of the first brigade per day: Total work done by the first brigade / Number of workers in the first brigade = Total work done by the first brigade / 12 2. Work rate of the second brigade per day: Total work done by the second brigade / Number of workers in the second brigade = Total work done by the second brigade / 21 3. Total work rate of both brigades per day: Work rate of the first brigade per day + Work rate of the second brigade per day 4. Total work done by both brigades in 10 days: Total work rate of both brigades per day * 10 5. Remaining work after 10 days: Total work required - Total work done by both brigades in 10 days 6. Work rate of the combined brigades after 12 workers join the first brigade: (Work rate of the first brigade per day * Number of workers in the first brigade) + (Work rate of the second brigade per day * (Number of workers in the second brigade - 12)) 7. Number of days required to complete the remaining work with the combined brigades: Remaining work after 10 days / Work rate of the combined brigades

Let's calculate the values using the given information:

1. Work rate of the first brigade per day: Total work done by the first brigade / Number of workers in the first brigade = Total work done by the first brigade / 12 2. Work rate of the second brigade per day: Total work done by the second brigade / Number of workers in the second brigade = Total work done by the second brigade / 21 3. Total work rate of both brigades per day: Work rate of the first brigade per day + Work rate of the second brigade per day 4. Total work done by both brigades in 10 days: Total work rate of both brigades per day * 10 5. Remaining work after 10 days: Total work required - Total work done by both brigades in 10 days 6. Work rate of the combined brigades after 12 workers join the first brigade: (Work rate of the first brigade per day * Number of workers in the first brigade) + (Work rate of the second brigade per day * (Number of workers in the second brigade - 12)) 7. Number of days required to complete the remaining work with the combined brigades: Remaining work after 10 days / Work rate of the combined brigades

Let's calculate the values using the given information:

1. Work rate of the first brigade per day: Total work done by the first brigade / Number of workers in the first brigade = Total work done by the first brigade / 12 2. Work rate of the second brigade per day: Total work done by the second brigade / Number of workers in the second brigade = Total work done by the second brigade / 21 3. Total work rate of both brigades per day: Work rate of the first brigade per day + Work rate of the second brigade per day 4. Total work done by both brigades in 10 days: Total work rate of both brigades per day * 10 5. Remaining work after 10 days: Total work required - Total work done by both brigades in 10 days 6. Work rate of the combined brigades after 12 workers join the first brigade: (Work rate of the first brigade per day * Number of workers in the first brigade) + (Work rate of the second brigade per day * (Number of workers in the second brigade - 12)) 7. Number of days required to complete the remaining work with the combined brigades: **Remaining work after 10 days