Question

Двое рабочих работая вместе могут окончить некоторую работу за 12 дней.после 8 дней совместной работы один из них заболел.и другой окончил работу один,проработав еще 5 дней.за сколько дней каждый из них может выполнить работу отдельно?

Answer 1

Введём понятие "производительность труда" каждого рабочего - то есть какую часть всей работы сделает рабочий (или оба вместе) за один день.
Из условия задачи сразу можно сказать: производительность двух рабочих вместе равна 1/12.
Работая с такой отдачей, они за 8 дней сделали:
$8 * \frac{1}{12} =\frac{8}{12} = \frac{2}{3}$ всего объёма работ.
После этого им осталось сделать $1- \frac{2}{3} =\frac{1}{3}$ работы, но тут один заболел.
Второй сделал 1/3 работы за 5 дней, значит его производительность равна
$\frac{1}{3} : 5 =\frac{1}{15}$
Теперь можем найти производительность первого:
$\frac{1}{12} - \frac{1}{15} =\frac{15-12}{15*12} =\frac{1}{60}$
Ответ: 1/15 и 1/60

Answer 2

Problem Analysis

Two workers working together can complete a certain job in 12 days. After 8 days of working together, one of them falls ill, and the other completes the job alone in 5 more days. We need to determine how many days each worker would take to complete the job individually.

Solution

Let's assume that the first worker's rate of work is represented by x (in terms of the fraction of the job completed per day) and the second worker's rate of work is represented by y.

From the given information, we can set up the following equations:

Equation 1: 12x + 12y = 1 (since the two workers can complete the job in 12 days)

Equation 2: 8x + 8y = 8/12 (since they worked together for 8 days and completed a fraction of the job)

Equation 3: 5x = 1 - (8/12) (since the second worker completed the remaining fraction of the job in 5 days)

Now, let's solve these equations to find the values of x and y.

Solving the Equations

To solve the system of equations, we can use the method of substitution.

From Equation 2, we can express x in terms of y:

x = (8/12 - 8y)/8

Substituting this value of x into Equation 1, we get:

(12(8/12 - 8y)/8) + 12y = 1

Simplifying the equation:

8(8/12 - 8y) + 12y = 1

64/12 - 64y + 12y = 1

64/12 - 52y = 1

-52y = 1 - 64/12

-52y = 12/12 - 64/12

-52y = -52/12

y = (-52/12) / -52

y = 1/12

Now that we have the value of y, we can substitute it back into Equation 2 to find the value of x:

8x + 8(1/12) = 8/12

8x + 2/3 = 2/3

8x = 2/3 - 2/3

8x = 0

x = 0

Conclusion

After solving the equations, we find that the first worker's rate of work (x) is 0, and the second worker's rate of work (y) is 1/12.

Therefore, the first worker would take infinity days to complete the job individually (since their rate of work is 0), and the second worker would take 12 days to complete the job individually.

Please note that the first worker's rate of work being 0 means that they are unable to complete the job on their own.

Let me know if there's anything else I can help you with!