The answer isn't as simple as you might think. You need to take your car through a driving cycle, which is different for every car manufacturer/model/engine type/etc.
Basically, your emission system monitors the status of your various emissions-related components (catalytic converter, O2 sensors, etc). When something is repaired, and the system is reset, it needs time to monitor these different parts (driving cycle) to make sure they are all functioning properly.
A service manual for your particular car (or sometimes a helpful technician at your dealership) could tell you what's involved in putting your car through a complete cycle - it's not just hours or distance driven.
For example, on my 97 honda: maintaining a speed of 45mph for 60 seconds is one of the steps needed to be checked off, another is a cold start and idle. There can be only several, or many depending on how complicated your particular system is.
The tech likely told you 3 days and 80 miles because during that time, your normal driving is likely to meet all the requirements of the testing cycle.
You can always get an autozone or similar place to test it for free, and make sure all your monitors are set to "ready" - this indicates that all the components have been tested.
Hope that helps!