Question

Двое рабочих работая вместе завершили работу за 6 днейСколько дней потребовалось бы каждому рабочему на выполнение этой работы если одному для этого требуется на 5 дней меньше чем другому??? Это 8 класс)) решите поже)^-^быстро)

Answer 1

Пусть вся работа 1
Путь одному рабочему на всю работу нужно х дней, тогда второму (х-5) дней.
Т.к. первый делает всю работу за х дней, то за 1 день он делает 1/х часть работы
Т.к. второй рабочий делает всю работу за (х-5) дней , то за 1 день он делает 1/(х-5) часть работы
Работали рабочие вместе 6 дней, значит они сделали вместе 6/х+6/(х-5), что по условию задачи является всей работой, получим уравнение
6/х+6/(х-5)=1
6*(х-5)+6х=х(х-5)
6х-30+6х=х²-5х
х²-17х+30=0
D=(-17)²-4*1*30=169=(13)²
х₁=(17+13)/2=15,
 х₂=(17-13)/2=2(посторонний корень, не удовлетворет условию задачи)
Т.о. первый рабочий может сделать всю работу сам за 15 дней, второй за 15-5=10 дней
Ответ: 15 дней и 5 дней

Answer 2

Problem Analysis

We are given that two workers completed a job together in 6 days. We need to determine how many days each worker would take to complete the job individually if one worker takes 5 days less than the other.

Solution

Let's assume that one worker takes x days to complete the job. According to the given information, the other worker would take x + 5 days to complete the job.

To find the solution, we can set up an equation based on the work rate of each worker. The work rate is inversely proportional to the number of days taken to complete the job. Therefore, the equation can be written as:

1/x + 1/(x + 5) = 1/6

To solve this equation, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 6x(x + 5). This will eliminate the fractions:

6(x + 5) + 6x = x(x + 5)

Simplifying the equation:

6x + 30 + 6x = x^2 + 5x

Combining like terms:

12x + 30 = x^2 + 5x

Rearranging the equation:

x^2 - 7x - 30 = 0

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

Quadratic Equation Solution

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation x^2 - 7x - 30 = 0, a = 1, b = -7, and c = -30.

Substituting the values into the quadratic formula:

x = (-(-7) ± √((-7)^2 - 4(1)(-30))) / (2(1))

Simplifying:

x = (7 ± √(49 + 120)) / 2

x = (7 ± √169) / 2

x = (7 ± 13) / 2

We have two possible solutions for x:

1. x = (7 + 13) / 2 = 20 / 2 = 10 2. x = (7 - 13) / 2 = -6 / 2 = -3

Since the number of days cannot be negative, we discard the second solution.

Therefore, one worker would take 10 days to complete the job, and the other worker would take 10 + 5 = 15 days to complete the job.

Answer

If one worker takes 5 days less than the other worker to complete the job, and they completed the job together in 6 days, then one worker would take 10 days to complete the job, and the other worker would take 15 days to complete the job.