Five printers will take 40 minutes to complete a valid magazine. The calculation is based on the inverse relationship between the number of printers and the time taken, resulting in a time reduction by a factor of 5.
Let's denote the time it takes for one printer to complete a valid magazine as T. The given information states that two printers together take 100 minutes, so the combined rate is 1/100 of the magazine per minute.
Therefore, the rate of one printer is 1/200 of the magazine per minute. Now, let t represent the time it takes for five printers to complete the magazine. The combined rate of five printers is
5 × 1/200 = 1/40 of the magazine per minute.
Now, we can set up the equation:
Rate × Time=Work
For five printers:
1/40 × t=1
Solving for t:
t=40
Thus, it will take five printers 40 minutes to complete a valid magazine.