This relates to a personal pet issue of mine -- schools like to run surveys asking how much time you spend on homework. But, as far as I can see, the question is ill-posed.
Take a non-hypothetical example: I'm given a math assignment, with the problem "prove (something complicated)". I look over the assignment, think for a few seconds about the problem, think "nah, that won't work", fail to come up with a different approach, and file it away somewhere in favor of surfing the net and watching my roommates play old console RPGs.
Days later, a new approach occurs to me and I come back to the assignment. This time I'm able to prove (something complicated). Writing out the proof takes 20 minutes.
How long did I spend on that question? I wasn't able to do the work immediately, so "21 minutes" can't be right. But I probably didn't actually need to spend several days having it in the back of my mind either. Maybe if I'd been confined in a little room with just me and the assignment I would have had it done in two hours, or five (really frustrating) hours. There's just no way to measure how long I spent "working". My quality of life goes up if I take the approach of "don't sit down to work until the solution serendipitously occurs to you", but, in an analogous situation, my boss might be a lot happier confining me in a room to sit "unproductively" for 5 hours and write ("productively") for 20 minutes.
Take a non-hypothetical example: I'm given a math assignment, with the problem "prove (something complicated)". I look over the assignment, think for a few seconds about the problem, think "nah, that won't work", fail to come up with a different approach, and file it away somewhere in favor of surfing the net and watching my roommates play old console RPGs.
Days later, a new approach occurs to me and I come back to the assignment. This time I'm able to prove (something complicated). Writing out the proof takes 20 minutes.
How long did I spend on that question? I wasn't able to do the work immediately, so "21 minutes" can't be right. But I probably didn't actually need to spend several days having it in the back of my mind either. Maybe if I'd been confined in a little room with just me and the assignment I would have had it done in two hours, or five (really frustrating) hours. There's just no way to measure how long I spent "working". My quality of life goes up if I take the approach of "don't sit down to work until the solution serendipitously occurs to you", but, in an analogous situation, my boss might be a lot happier confining me in a room to sit "unproductively" for 5 hours and write ("productively") for 20 minutes.