Final answer:
By determining the work rate of each group of workers and combining them, we calculate that the team of 2 skilled, 6 semiskilled, and 5 unskilled workers will take approximately 15 days to build the wall, corresponding to answer choice D.
Step-by-step explanation:
To find out how long it will take 2 skilled, 6 semiskilled, and 5 unskilled workers to build the wall, we first need to determine the work rate of each group of workers individually. The work rate is typically expressed in terms of walls built per day.
For skilled workers: 5 skilled workers can build 1 wall in 20 days. So, the work rate of one skilled worker is 1 wall / (5 skilled workers × 20 days) = 1/100 wall per day.
For semiskilled workers: 8 semiskilled workers can build 1 wall in 25 days. So, the work rate for one semiskilled worker is 1 wall / (8 semiskilled workers × 25 days) = 1/200 wall per day.
For unskilled workers: 10 unskilled workers can build 1 wall in 30 days. So, the work rate for one unskilled worker is 1 wall / (10 unskilled workers × 30 days) = 1/300 wall per day.
Now, let's calculate the combined work rate of the team:
- 2 skilled workers' rate: 2 × 1/100 = 1/50 wall per day
- 6 semiskilled workers' rate: 6 × 1/200 = 1/33.33 wall per day
- 5 unskilled workers' rate: 5 × 1/300 = 1/60 wall per day
Adding these rates gives the team's combined work rate: 1/50 + 1/33.33 + 1/60 = 0.02 + 0.03 + 0.016667 ≈ 0.066667 wall per day. To find out how many days it takes to build one wall, we take the reciprocal of the combined work rate: 1 / 0.066667 ≈ 15 days.
Therefore, the team will take 15 days to build the wall, which corresponds to answer choice D.