Question

2 бригады, работая совместно, могут выполнить некоторые задания за 3 ч. 36 мин. Сколько времени затратит на выполнение этого задания каждая бригада, работая в отдельности, если известно, что первой бригаде требуется для этого на 3 часа больше времени, чем второй.

Answer 1

 

Примемвсе задание за единицу.

Пусть 1-я бригада выполнит всю работу за х часов
2-я за х-3
производительность 1-ой бригады 1:х задания в час
2-й 1:(х-3)

общая производительность
1:х + 1:(х-3)=(2х-3):(х²-3х)

Все задание, работая вместе, они выполнят за 

1:{(2х-3):(х²-3х)}  часов 

(х²-3х):(2х-3)=3 ч.36 мин

(х²-3х):(2х-3)=36:10

Умножим на 10(2х-3) обе стороны уравнения
36(2х-3)=10(х²-3х)
72х-108=10х²-30х
10х²-102х+108=0
5х²-51х+54=0

D=b²-4ac=--51²-4·5·54=1521
х₁=9
х₂=1,2 (не подходит)

9ч время первой бригады
6ч-время второй бригады

 

Проверка:
Производительность общая
1/9+1/6=4/36+6/36=10/36
Работая вместе, бригады задание выполнят за
1:10/36=36:10=3,6 часа или 3 часа 36 мин. 

 

 

 

 

 

Answer 2

Problem Analysis

We are given that two teams working together can complete a task in 3 hours and 36 minutes. We need to find out how much time each team will take to complete the task individually, given that the first team takes 3 hours longer than the second team.

Solution

Let's assume that the second team takes x hours to complete the task. According to the given information, the first team takes 3 hours longer than the second team, so the first team will take (x + 3) hours to complete the task.

To find the time taken by each team individually, we can set up the following equation:

1/(x + 3) + 1/x = 1/(3 hours and 36 minutes)

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can convert 3 hours and 36 minutes into hours. Since 1 hour is equal to 60 minutes, 36 minutes is equal to 36/60 = 0.6 hours.

Substituting the values into the equation:

1/(x + 3) + 1/x = 1/(3 + 0.6) 1/(x + 3) + 1/x = 1/3.6

To simplify the equation, we can multiply both sides by (x)(x + 3)(3.6):

3.6(x) + 3.6(x + 3) = (x)(x + 3)

Expanding and simplifying:

3.6x + 10.8 = x^2 + 3x

Rearranging the equation:

x^2 + 3x - 3.6x - 10.8 = 0 x^2 - 0.6x - 10.8 = 0

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

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -0.6, and c = -10.8.

Substituting the values into the quadratic formula:

x = (-(-0.6) ± √((-0.6)^2 - 4(1)(-10.8))) / (2(1))

Simplifying:

x = (0.6 ± √(0.36 + 43.2)) / 2 x = (0.6 ± √43.56) / 2

Calculating the square root:

x = (0.6 ± 6.6) / 2

Now, we have two possible values for x:

x1 = (0.6 + 6.6) / 2 x1 = 7.2 / 2 x1 = 3.6

x2 = (0.6 - 6.6) / 2 x2 = -6 / 2 x2 = -3

Since time cannot be negative, we discard the negative value of x.

Therefore, the second team will take 3.6 hours to complete the task individually, and the first team will take 3.6 + 3 = 6.6 hours to complete the task individually.

Answer

Each team, working individually, will take the following amount of time to complete the task: - The second team: 3.6 hours - The first team: 6.6 hours

Note: The calculations were made using the quadratic formula and the given information.