Question

ПОМОГИТЕ!!!СРОЧНО!!!двое рабочих могут выполнить некоторую работу за 7 дней при условии, что второй приступит к ней на 2 дня позже первого. Если бы ту же работу каждый выполнял в одиночку, то первому потребовалось бы на 4 дня больше, чем второму. За сколько дней каждый рабочий мог бы выполнить эту работу?

Answer 1

Пусть за х дней второй рабочий может один выполнить всю работу
х+4 дня нужно первому рабочему, чтобы выполнить всю работу
примем всю работу за 1 часть
7/ (х+4) часть работы выполнил первый рабочий за 7 часов
7-2 =5 часов работал второй рабочий
5/х часть работы выполнил второй рабочий за 5 часов
так как они выполнили всю работу, то
7/ (х+4) +5/х =1 или
х² -8х -20 =0 или
х= 10 или х= -2 ( посторонний корень)
Ответ
10+4 =14 дней нужно первому рабочему, чтобы выполнить всю работу одному
10 дней нужно второму рабочему, чтобы выполнить всю работу одному

Answer 2

Problem Analysis

We are given that two workers can complete a certain job in 7 days, with the second worker starting 2 days after the first worker. If each worker were to work alone, the first worker would take 4 days longer than the second worker to complete the job. We need to determine how many days each worker would take to complete the job individually.

Solution

Let's assume that the first worker can complete the job in x days. According to the given information, the second worker would take x + 4 days to complete the job.

We are also given that when both workers work together, they can complete the job in 7 days. This means that their combined work rate is 1/7 of the job per day.

To solve this problem, we can set up the following equation based on the work rates:

1/x + 1/(x + 4) = 1/7

Let's solve this equation to find the value of x, which represents the number of days the first worker would take to complete the job.

Calculation

To solve the equation 1/x + 1/(x + 4) = 1/7, we can multiply both sides of the equation by 7x(x + 4) to eliminate the denominators:

7(x + 4) + 7x = x(x + 4)

Simplifying the equation:

7x + 28 + 7x = x^2 + 4x

Combining like terms:

14x + 28 = x^2 + 4x

Rearranging the equation:

x^2 - 10x - 28 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 10x - 28 = 0, the values of a, b, and c are:

a = 1, b = -10, c = -28

Substituting these values into the quadratic formula:

x = (-(-10) ± √((-10)^2 - 4(1)(-28))) / (2(1))

Simplifying:

x = (10 ± √(100 + 112)) / 2

x = (10 ± √212) / 2

x = (10 ± 2√53) / 2

Simplifying further:

x = 5 ± √53

Therefore, the possible values for x are:

x = 5 + √53 or x = 5 - √53

Since the number of days cannot be negative, we can discard the solution x = 5 - √53.

So, the first worker would take approximately 5 + √53 days to complete the job individually.

To find the number of days the second worker would take, we can substitute this value into the equation x + 4:

x + 4 = (5 + √53) + 4 = 9 + √53

Therefore, the second worker would take approximately 9 + √53 days to complete the job individually.

Answer

Based on the given information, the first worker would take approximately 5 + √53 days to complete the job individually, and the second worker would take approximately 9 + √53 days to complete the job individually.