Is the exact time it takes to evaluate 27 plus 72exact time it takes to evaluate 27+72 discrete or continuous?

Time is continuous.

 If it was possible to measure EXACTLY the time it takes a person (or group of people) to evaluate 27 + 72 (=99), the time(s) people took could be 2 seconds, 3 seconds, 2.5 seconds, 2.25 seconds, 2.22 seconds, 2.2199999 seconds... In other words, any value is possible when measuring "exact" time elapsed.

However, people are limited by the tools they use. There isn't a tool without limits in its ability to measure time elapsed. For example, is the stopwatch accurate to 1/100th of a second? 1/1000th of a second? At some point it reaches its limit. The constraints of the tool being used to measure are going to, in fact, cause data to be "discrete."

I'm 90% sure you're teacher is looking for "continuous" as the solution though. So don't bring up "discrete" unless you feel like you'll be able to confidently explain the second paragraph above.