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Difficulty: EasyRatios, Rates, and Proportions

Printer X prints at a constant rate of 6060 pages per minute, and Printer Y prints at a constant rate of 4040 pages per minute. If both printers operate simultaneously at their respective constant rates, which of the following statements must be true? Select all that apply.

  1. Working together, the two printers print 100100 pages in 11 minute.Answer
  2. Printer X prints 60%60\% of the total number of pages produced when both printers operate for the same duration.Answer
  3. C
    The ratio of the time taken by Printer Y to print a job to the time taken by Printer X to print the same job is 2:32:3.
  4. Working together, the two printers require 55 minutes to print 500500 pages.Answer
  5. E
    The combined printing rate of the two printers working together is 5050 pages per minute.

Answer

The correct statements are that working together the printers print 100 pages in 1 minute, Printer X prints 60% of the total pages, and working together they require 5 minutes to print 500 pages.
The combined rate is 60+40=10060 + 40 = 100 pages per minute. In 11 minute, 100100 pages are printed. In 55 minutes, 5×100=5005 \times 100 = 500 pages are printed. Out of every 100100 pages, Printer X produces 6060, which corresponds to 60%60\%.

Step-by-Step Solution

1
Calculate the combined rate of both printers
Combined rate = 60+40=10060 + 40 = 100 pages per minute
When two entities work together simultaneously, their work rates add directly.
2
Evaluate the proportion of total output printed by Printer X
Proportion = 6060+40=60100=60%\frac{60}{60 + 40} = \frac{60}{100} = 60\%
The fraction of work done by one printer is its rate divided by the total combined rate.
3
Determine the time ratio between Printer Y and Printer X for a fixed job
Time ratio Y : X = 1/401/60=6040=3:2\frac{1/40}{1/60} = \frac{60}{40} = 3:2
Time required for a fixed task is inversely proportional to the work rate.
4
Calculate time needed for 500 pages working together
Time = 500 pages100 pages/min=5 minutes\frac{500\text{ pages}}{100\text{ pages/min}} = 5\text{ minutes}
Time equals total work divided by combined rate.

Key Concept

Additive work rates and inverse relationship between rate and time in ratio problems
Estimated Time:1m 0s
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Topics

Ratios, Rates, and Proportions

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