It will take an apprentice 15 days longer than a qualified printer to complete a job. However if 3 apprentices and two qualified printers work together the job can be completed in 3 1/8 days. how long would it take one apprentice to do the job
q = a + 15
3a + 2q = 3 1/8
Substitute a+15 for q in the second equation and solve for a.
To solve this problem, we will first determine how long it takes one qualified printer to complete the job. Let's assign a variable to represent the time it takes for one qualified printer to complete the job. Let's call this variable "P" (for printer).
Next, since an apprentice takes 15 days longer than a qualified printer, we can represent the time it takes for an apprentice to complete the job as "P + 15" (since P represents the time for a qualified printer).
Now, let's consider the scenario where 3 apprentices and 2 qualified printers work together. We are given that they can complete the job in 3 1/8 days. We can convert "3 1/8" into the fraction of days: 25/8.
Using this information, we can create an equation to represent the work rate of the combined team:
(3 * (P + 15)) + (2 * P) = 25/8
Now, let's solve this equation to find the value of P, which represents the time it takes for one qualified printer to complete the job:
(3P + 45) + (2P) = 25/8
5P + 45 = 25/8
To isolate P, we can subtract 45 from both sides:
5P = 25/8 - 45
To simplify the right side, we need to convert 25/8 into a fraction with a common denominator of 8:
5P = 25/8 - 360/8
5P = -335/8
Now, to get the value of P, we can divide both sides by 5:
P = (-335/8) ÷ 5
P = -335/40
P = -8.375
Since time cannot be negative, we discard the negative solution. Therefore, one qualified printer takes -8.375 days to complete the job, which is not possible.
Hence, it is not feasible for one apprentice alone to complete the job.