No, there's no mechanism in the Word file format itself to store this information. There's the file system metadata (Created/Accessed/Modified time) which tells

No, there's no mechanism in the Word file format itself to store this information. There's the file system metadata (Created/Accessed/Modified time) which tells you for how long the file was open before being saved. However, file system metadata is likely to be lost when you submit the document. Ultimately, you could not prevent this timer from being spoofed unless you installed rootkits on the students' computers, and unfortunately (for the security and privacy of students) rootkits are what is often used.