Question

Две Бригады,работая вместе,выполнили работу за 12 дней.Сколько дней потребовалось бы каждой бригаде на выполнение этой работы,если одной из них на это требуется на 10 дней меньше,чем другой?

Answer 1

Вся работа принимается за 1
производительность труда первой бригады 1\х 
производительность труда второй 1/(х+10) 
производительность при совместной работе 1\12 
 получаем уравнение:
(1/х+1)/(х+10)=12 
12(х+10+х) =х*(х+10)
12х+120+12х-х^2-10х=0
14х-х^2+120=0
х^2-14х-120=0
Д=196+480=672
х1=20 
х2=-6 (не удовлетворяет условию задачи)
х1=20 (первая бригада)
х2=20+10=30(вторая бригада)

Answer 2

Solution:

To solve this problem, we can use the concept of work rates and time. Let's denote the time taken by the first brigade as x days and the time taken by the second brigade as x - 10 days.

We know that the combined work rate of both brigades is 1 job per 12 days. Using this information, we can set up the following equation:

1/x + 1/(x - 10) = 1/12

Now, let's solve for x to find the time taken by each brigade to complete the work individually.

Calculation:

Using the equation 1/x + 1/(x - 10) = 1/12, we can solve for x:

1/x + 1/(x - 10) = 1/12

Multiplying through by 12x(x - 10) to clear the fractions:

12(x - 10) + 12x = x(x - 10)
12x - 120 + 12x = x^2 - 10x
24x - 120 = x^2 - 10x
0 = x^2 - 10x - 24x + 120
0 = x^2 - 34x + 120

Using the quadratic formula to solve for x:

x = (-(-34) ± √((-34)^2 - 4*1*120)) / (2*1)
x = (34 ± √(1156 - 480)) / 2
x = (34 ± √676) / 2
x = (34 ± 26) / 2

So, we have two possible values for x:

1. x = (34 + 26) / 2 = 60 / 2 = 30 2. x = (34 - 26) / 2 = 8 / 2 = 4

Since the time taken by the first brigade cannot be less than the time taken by the second brigade minus 10 days, the only valid solution is x = 30.

Answer:

Therefore, the first brigade would take 30 days to complete the work, and the second brigade would take 20 days to complete the work.