Question

Две бригады, работая совместно , закончили строительство водоема за 12 дней . Сколько дней потребовалось бы на строительство водоема каждой бригаде в отдельности , если одна из них могла бы выполнить работу на 10 дней раньше? Помогите решить плиииииз

Answer 1

За х дней выполнит одна бригада работу
за х+10 - выполнит вторая
1/х - столько выполнит работы 1-я бригада за один день
1/х +10 - вторая бригада за 1 день
(1/х+(1/х+10)) - выполнят обе за один день
(1/х+1/х+10) *12=1
(1/х+1/х+10)=1/12
х+10=х/х+10=1/12
2х+10*12=х2+10х
24х+120=х2+10х
х2-14х-120=0
Дальше пропускаю действие,  не знаю как квадратный корень  тут вписать (но это уже не сложно), и получается
Одной 20, второй 30

Answer 2

Problem Analysis

We are given that two brigades working together completed the construction of a reservoir in 12 days. We need to determine how many days it would take for each brigade to complete the construction individually if one of them could finish the work 10 days earlier.

Solution

Let's assume that the first brigade can complete the construction in x days. Since the second brigade can finish the work 10 days earlier, it would take (x - 10) days for the second brigade to complete the construction.

According to the given information, when both brigades work together, they complete the construction in 12 days. We can set up the following equation based on the work rates:

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

To solve this equation, we can multiply both sides by 12x(x - 10) to eliminate the denominators:

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

Simplifying the equation:

12x - 120 + 12x = x^2 - 10x

Rearranging the terms:

x^2 - 34x + 120 = 0

Now we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -34, and c = 120, we can calculate the values of x.

Calculating the discriminant, D = b^2 - 4ac:

D = (-34)^2 - 4(1)(120) = 1156 - 480 = 676

Since the discriminant is positive, there are two distinct real solutions for x.

Using the quadratic formula:

x = (-(-34) ± √(676)) / (2(1)) x = (34 ± 26) / 2

Simplifying:

x1 = (34 + 26) / 2 = 60 / 2 = 30 x2 = (34 - 26) / 2 = 8 / 2 = 4

Therefore, the first brigade would take 30 days to complete the construction individually, and the second brigade would take 4 days to complete the construction individually.

Answer

If the first brigade could complete the work in 30 days, and the second brigade could complete the work 10 days earlier, it would take 20 days for the second brigade to complete the construction individually.

Note: Please double-check the calculations for accuracy.