Question

Одна бригада может выполнить задание за 40 дней, а другая за 50 дней. Хватит ли им 22 дней для выполнения того же задания при совместной работе? помогите

Answer 1

Пусть все задание =1
первая бригада в день выполняет 1/40 часть задания
вторая - 1/50 часть
работая вместе в день они выполнят 1/50+1/40=(50+40)/200=9/200 часть задания 
за 22 дня они выполнят 22*9/200=198/200 = 0,99 часть задания
то есть им не хватит 22 дня

Answer 2

Problem Analysis

We are given two brigades that can complete a task in 40 days and 50 days, respectively. We need to determine if they can complete the same task in 22 days when working together.

Solution

To solve this problem, we can calculate the combined work rate of the two brigades and see if it is sufficient to complete the task in 22 days.

Let's denote the work rate of the first brigade as B1 (in units of work per day) and the work rate of the second brigade as B2 (in units of work per day). The work rate is inversely proportional to the number of days required to complete the task.

The work rate of the first brigade is given by B1 = 1/40 (since they can complete the task in 40 days), and the work rate of the second brigade is given by B2 = 1/50 (since they can complete the task in 50 days).

To find the combined work rate of the two brigades, we can add their individual work rates: B_combined = B1 + B2.

Now, let's calculate the combined work rate:

B_combined = 1/40 + 1/50

To determine if the two brigades can complete the task in 22 days, we need to check if the combined work rate is sufficient. If the combined work rate is greater than or equal to 1/22, then the two brigades can complete the task in 22 days.

Let's calculate the combined work rate:

B_combined = 1/40 + 1/50 = 0.025 + 0.02 = 0.045

Since B_combined = 0.045 is greater than 1/22 = 0.045, the two brigades can complete the task in 22 days when working together.

Conclusion

Yes, the two brigades will be able to complete the task in 22 days when working together.