A painting job can be completed by 6 painters in 28 days. If 24 more painters join the team 8 days after starting work on the job, then how many more days are required to complete the job?
-
5
-
6
-
3
-
4
Total work is 6 * 28 = 168 man-days. After 8 days, 6 * 8 = 48 man-days are done. Remaining work = 168 - 48 = 120 man-days. New team size = 6 + 24 = 30 painters. Days needed = 120 / 30 = 4 days.
To solve this question, we need to determine the rate at which the painters work and then use that information to calculate the additional time required to complete the job when 24 more painters join the team.
Let's assume that the rate at which the 6 painters work is represented by the variable "R."
We know that the job can be completed by 6 painters in 28 days. So, the total work involved in the job is equal to 6 * 28 = 168 "painter-days."
Now, let's consider the scenario after 8 days when 24 more painters join the team. At this point, the work done by the 6 painters is equal to 6 * 8 = 48 "painter-days."
The remaining work to be done is equal to 168 - 48 = 120 "painter-days."
Since the number of painters has increased to 6 + 24 = 30, the rate at which the painters work can be represented by 30 * R.
Using the concept of "work done = rate * time," we can set up the equation:
120 = 30 * R * T,
where T is the additional time required to complete the job.
Simplifying the equation, we get:
120 = 30 * R * T, 4 = R * T.
Since we don't have any information about the rate at which the painters work, we can't determine the value of R. However, we can determine the value of T.
Therefore, the correct answer is D) 4.