Question

Двое рабочих, выполняя определённую работу вместе могут завершить его за 12 дней. Если сначала будет работать только один из них, а после выполнения половины работы его сменит другой, то всё задание будет выполнено за 25 дней. За сколько дней каждый из рабочих выполнит это задание?

Answer 1

Первый выполнит за 24 дня если не заболеет
второй за 26 дней

Answer 2

Task Description

Two workers can complete a certain task together in 12 days. If one of them works alone initially and is then replaced by the other after completing half of the work, the entire task will be completed in 25 days. The question is: how many days will each worker take to complete the task individually?

Solution

Let's assume that the total work to be done is represented by the variable W.

From the given information, we can derive the following equations:

1. When both workers work together, they can complete the task in 12 days. This can be represented as:

1/12 of the work done by both workers in one day = W

2. When the first worker works alone for half of the task and then is replaced by the second worker, they complete the task in 25 days. This can be represented as:

(1/2) of the work done by the first worker in one day + (1/2) of the work done by the second worker in one day = W

To solve for the number of days each worker takes to complete the task individually, we can set up a system of equations using the above information.

Let's assume that the first worker completes the task in x days and the second worker completes the task in y days.

From equation 1, we have:

1/x + 1/y = 1/12 ----(Equation 1)

From equation 2, we have:

(1/2)x + (1/2)y = 1/25 ----(Equation 2)

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:

From Equation 1, we can express 1/y in terms of x:

1/y = 1/12 - 1/x

Substituting this value in Equation 2, we get:

(1/2)x + (1/2)(1/12 - 1/x) = 1/25

Simplifying the equation:

(1/2)x + (1/24 - 1/(2x)) = 1/25

Multiplying through by the common denominator of 24x:

12x^2 + 12 - 12x = x

Rearranging the equation:

12x^2 - 13x + 12 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c:

x = (-(-13) ± sqrt((-13)^2 - 4(12)(12))) / (2(12))

Simplifying the equation:

x = (13 ± sqrt(169 - 576)) / 24

x = (13 ± sqrt(-407)) / 24

Since the square root of a negative number is not a real number, there are no real solutions for x. This means that the given information is inconsistent and cannot be solved.

Therefore, it is not possible to determine the number of days each worker will take to complete the task individually based on the given information.

Please let me know if there is anything else I can help you with.