Two printers with a production head start

Core stretch

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.[1]
2. Form an equation in \(p\) and \(q\) to represent the first test.[2]

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.

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