Work Rate Problem: Two Printers

A printer can print \(200\) pages in \(3\) minutes. The printer needs to complete a task which will last for \(8\) hours. After \(2\) hours of printing, a new printer is used to speed up the process. The two printers then complete all the remaining copies of the task in \(2.5\) hours. Find the rate of the new printer.

The stated eight hours is the time the original printer would take working alone on the entire job. Both printers maintain constant printing rates.