The admin office at Queenstown Primary School has two printers. Printer A prints at 40 pages per minute and Printer B prints at 25 pages per minute. Printer A starts working alone. At some point, Printer B joins in and both printers work together until a total of 1,000 pages have been printed. Printer A printed 800 pages in total throughout the entire job. For how many minutes did Printer B operate?
Show Worked Solution
Worked Solution
Step 1: Find the total time Printer A operated (alone + together).
Printer A's total pages = 800, rate = 40 pages/min
Total time for A = 800 ÷ 40 = 20 minutes
Step 2: Let t = number of minutes both printers worked together.
Printer A's alone phase = (20 − t) minutes
Step 3: Write an equation for total pages printed.
Pages by A alone + Pages by both together = 1,000
40 × (20 − t) + (40 + 25) × t = 1,000
800 − 40t + 65t = 1,000
800 + 25t = 1,000
25t = 200
t = 8 minutes
Verification:
A alone (12 min): 40 × 12 = 480 pages
Both together (8 min): 65 × 8 = 520 pages
Total: 480 + 520 = 1,000 pages ✓
A's total: 480 + 40 × 8 = 480 + 320 = 800 pages ✓
Printer B operated for 8 minutes.
Correct answer: 8 min
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