How to collect users’ task completion times?

I have to do a cost benefit analysis for a project in work. To get funding, I need to prove that the task to be fixed is time-consuming for users. We will only need to test about 20 users, but we'll need multiple responses from each user.

Should I just send something to all users where, for example, they click "Start" then "End" and it records the times or duration between clicks?

What other tools, strategies, or methods are available for timing users in this way?