Question

Два работника, работая вместе, могут сделать работу за 12 дней. проработав вместе 10 дней, один из них заболел, другой закончил работу за 5 дней. сколько каждому потребуется времени, если будут работать по отдельности?

Answer 1

12-10=2
5/2=2,5
2,5*12=30
Ответ 30

Answer 2

Problem Analysis

We have two workers who can complete a job together in 12 days. However, after working together for 10 days, one of them falls ill and the other completes the job in 5 days. We need to determine how long it would take each worker to complete the job individually.

Solution

Let's assume that the first worker's rate of work is represented by x and the second worker's rate of work is represented by y. We can use the formula Work = Rate × Time to solve this problem.

From the given information, we know that: - The combined rate of work for both workers is 1/12 (since they can complete the job together in 12 days). - After working together for 10 days, the remaining work is completed by the second worker in 5 days.

Using these facts, we can set up the following equations:

Equation 1: 10(x + y) + 5y = 1 (The work done by both workers in 10 days, plus the work done by the second worker in the remaining 5 days, equals the total work, which is 1.)

Equation 2: x + y = 1/12 (The combined rate of work for both workers is 1/12.)

To solve these equations, we can use substitution or elimination. Let's use substitution:

From Equation 2, we can express x in terms of y: x = 1/12 - y

Substituting this value of x into Equation 1, we get: 10((1/12 - y) + y) + 5y = 1

Simplifying the equation: 10/12 + 5y = 1 5y = 1 - 10/12 5y = 1/12 y = 1/60

Now, we can substitute this value of y back into Equation 2 to find x: x + 1/60 = 1/12 x = 1/12 - 1/60 x = 5/60 - 1/60 x = 4/60 x = 1/15

Therefore, the first worker would take 1/15 of the job to complete on their own, and the second worker would take 1/60 of the job to complete on their own.

Answer

If the two workers were to work separately, the first worker would require 1/15 of the time to complete the job, and the second worker would require 1/60 of the time to complete the job.

Please let me know if anything is unclear or if you need further assistance!

Answer 3

Problem Analysis

We are given that two workers can complete a job in 12 days when working together. However, one of the workers falls ill after working together for 10 days, and the other worker completes the job in 5 days. We need to determine how long it would take each worker 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.

When the two workers work together for 10 days, they complete a fraction of the job equal to 10 times the combined rate of work: 10(x + y) = 1/12 After 10 days, one worker falls ill, and the other worker completes the remaining fraction of the job in 5 days: 5y = 1 - 10(x + y) We can solve these two equations to find the values of x and y.

Calculation

Let's solve the equations:

From equation 1: 10(x + y) = 1/12

Simplifying: 10x + 10y = 1/12

From equation 2: 5y = 1 - 10(x + y)

Simplifying: 5y = 1 - 10x - 10y 15y = 1 - 10x y = (1 - 10x)/15

Substituting the value of y in equation 1: 10x + 10((1 - 10x)/15) = 1/12

Simplifying: 10x + (2/3)(1 - 10x) = 1/12 10x + (2/3) - (20/3)x = 1/12 (10 - 20/3)x = 1/12 - 2/3 (30/3 - 20/3)x = 1/12 - 8/12 (10/3)x = -7/12 x = (-7/12) * (3/10) x = -7/40

Substituting the value of x in equation 2: 5y = 1 - 10(-7/40) - 10y 5y = 1 + 7/4 - 10y 15y = 4 + 7 - 40y 55y = 11 y = 11/55 y = 1/5

Answer

Therefore, the first worker would take 7/40 of a day (or approximately 0.175 days) to complete the job individually, and the second worker would take 1/5 of a day (or 0.2 days) to complete the job individually.

Please note that the calculations provided above are based on the given information and assumptions made.