Question

Две бригады,работая вместе ,выполняют работу за 6 ч.одной первой бригаде на ту же работу требуется на 9 ч больше,чем второй .За какое время может выполнить

Answer 1

1-работа
1/6-скорость работы двух бригад
х-время второй бригады
1/х--скорость работы 2й бригады
х+9-время первой бригады
1/(х+9)--скорость работы 1й бригады

1/х+1/(х+9)=1/6 умножим на 6 х(х+9)
6(х+9)+6х=х(х+9)
6х+54+6х=х²+9х
х²-3х-54=0
D = b² - 4ac = (-3)2 - 4·1·(-54) = 9 + 216 = 225
x1 = (3 - √225)/(2·1) = (3 - 15)/2 = -12/2 = -6 не подходит
x1 = (3 + √225)/(2·1) = (3+ 15)/2 = 18/2 = 9ч-время второй бригады
9+9=18ч--время 1й бригады

Answer 2

Problem Analysis

We are given that two brigades working together can complete a task in 6 hours. The first brigade takes 9 hours more than the second brigade to complete the same task. We need to determine how long it would take for the first brigade to complete the task alone.

Solution

Let's assume that the second brigade can complete the task in x hours. According to the given information, the first brigade takes 9 hours more than the second brigade, so the first brigade would take (x + 9) hours to complete the task alone.

When the two brigades work together, they can complete the task in 6 hours. This means that in 1 hour, they can complete 1/6th of the task.

To find the time it would take for the first brigade to complete the task alone, we can set up the following equation:

1/(x + 9) + 1/x = 1/6

Now, let's solve this equation to find the value of x, which represents the time it would take for the second brigade to complete the task alone.

Calculation

To solve the equation, we can multiply both sides by 6x(x + 9) to eliminate the denominators:

6x + 6(x + 9) = x(x + 9)

Simplifying the equation:

6x + 6x + 54 = x^2 + 9x

Combining like terms:

12x + 54 = x^2 + 9x

Rearranging the equation:

x^2 - 3x - 54 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -3, and c = -54.

Substituting the values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(1)(-54))) / (2(1))

Simplifying:

x = (3 ± √(9 + 216)) / 2

x = (3 ± √225) / 2

x = (3 ± 15) / 2

We have two possible solutions:

1. x = (3 + 15) / 2 = 18 / 2 = 9 2. x = (3 - 15) / 2 = -12 / 2 = -6

Since time cannot be negative, we discard the second solution.

Therefore, the second brigade can complete the task alone in 9 hours.

To find the time it would take for the first brigade to complete the task alone, we add 9 hours to the time taken by the second brigade:

Time taken by the first brigade = 9 + 9 = 18 hours

So, the first brigade can complete the task alone in 18 hours.

Answer

The first brigade can complete the task alone in 18 hours.