Two printers with a production head start

Two printers with a production head start

Secondary 2
TGM Original Questions

Printer A takes \(p\) seconds to print each page and Printer B takes \(q\) seconds to print each page. In a first test, each printer prints \(80\) pages from a standing start, and Printer A finishes \(1.6\) seconds before Printer B.

  1. Write down an expression, in terms of \(p\) and \(q\), for the difference between the two printing times.
  2. Form an equation in \(p\) and \(q\) to represent the first test.

In a second test, Printer B begins with \(10\) pages already printed and finishes its remaining \(70\) pages \(1.4\) seconds before Printer A finishes all \(80\) pages.

  1. Form another equation in \(p\) and \(q\) to represent the second test.
  2. Solve the equations obtained in (ii) and (iii) to find \(p\) and \(q\).
  3. Hence, calculate the time Printer B would take to print \(80\) pages from a standing start.

Solution:

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Answer:\(p=0.28\), \(q=0.30\) s/page; Printer B's 80-page time is 24 seconds.

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