Final answer:
To determine the time 11 men and 3 women need to complete the work, we set up equations based on their individual work rates derived from the information given and then solve these equations to find the answer. The correct answer is D. 16 days.
Step-by-step explanation:
The question asks how long it will take for 11 men and 3 women to complete a task given that 3 men and 4 women can complete it in 10 days, and 24 men and 2 women can complete it in 2 days. To solve this, we can set up two equations representing the work done by men and women, and use them to find the work rate of each group. Once we have the rates, we can calculate the time for 11 men and 3 women to finish the task.
Let's define M as the part of work one man can do in one day and W as the part of work one woman can do in one day. From the first condition, we know that:
3M + 4W = 1/10 (since they complete the job in 10 days)
From the second condition we know that:
24M + 2W = 1/2 (since they complete the job in 2 days)
We can now solve these two equations to find out the values of M and W. After finding M and W, we can plug in the values for 11 men and 3 women to find out how long they will take to complete the work. Let's suppose they will take X days to complete the work then:
11M + 3W = 1/X
By solving the above equations, we'll be able to find the value of X. The options given are:
- A. 2 days
- B. 4 days
- C. 8 days
- D. 16 days
Through the process of solving these linear equations, we will find the correct answer.