Final answer:
To find the time taken to complete the job, we can use the given information and solve for the number of women who worked on the job. Using the formula for the nth term of an arithmetic sequence, we can determine the number of terms in the sequence. By plugging in the given values, we can calculate the total number of days it took to complete the job.
Step-by-step explanation:
To find the time taken to complete the job, we need to determine the number of women who joined the group. Since 4 women started working on the job and a new woman joined every 4 days, we can use this information to calculate the total number of women who worked on the job. The sequence of the number of women who worked on the job after every 4 days is 4, 5, 6, 7, 8, ... This is an arithmetic sequence with a common difference of 1 and a first term of 4.
Using the formula for the nth term of an arithmetic sequence, we can calculate the number of terms:
an = a1 + (n - 1)d
Where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
Let's set an to be 10, which represents the number of women in total:
10 = 4 + (n - 1)(1)
Simplifying the equation, we get:
n = 7
Therefore, a total of 7 women worked on the job. Since there were 10 women in total, we can calculate the number of days it took to complete the job using the formula:
Number of days = (Total number of women * Number of days for the job) / Number of women working per day
Plugging in the given values, we get:
Number of days = (10 * 12) / 7 = 17.14
The job took approximately 17.14 days to complete.