A new printer can print a set of newsletters in 15 minutes l

A new printer can print a set of newsletters in 15 minutes less than an older printer can. If both printers work simultaneously, they can print the set of newsletters in 40 minutes. How long does it take the older printer alone to print the set of newsletters? It takes the old printer approximately minutes to print the set of newsletters.

Solution

Let x be the numberof minutes that the old printer takes to print the newsletter alone. Then, the time taken by the new printer to print the newsletter alone is x - 15 minutes. When the two printers work together, the job is done in 40 minutes. The old printer finishes 1/x of the job in 1 minute and the new printer finishes 1/ (x -15) of the job in 1 minute. Therefore, the 2 printers , working simultaneously, finish ( 1/x) + (1/x -15) of the job in 1 minute. Therefore, ( 1/x) + (1/x -15) = 1/40 or, (2x -15)/ x ( x -15) = 1/40 or, 40(2x -15) = x ( x -15) or, 80 x - 600 = x² -15x or, x² - 95x + 600 = 0 . Therefore, x = [ 95 ± { (95)² - 4*1*600} ]/2*1 = [95 ± (9025 - 2400)]/2 = (95 ± 6625)/2 = ( 95 ± 81.39)/2 . Thus, either x = 6.805 minutes or, x = 88.20 mintes. Now, x cannot be 6.805 minutes, because then the new printer will take negative time to print the newsletter which is not possible. Therefore x = 88.20 minutes. Thus, the old printer takes approximately 88.20 minutes to print the set of newsletters.