Forty Minutes No Ideas

You are 40 minutes into a problem. In the last 10 of those you produced two new ideas and rejected both, and you have nothing else queued. The USACO Guide's contributors give different numbers: Darren Yao says read the solution after 15 to 20 minutes of no meaningful progress at the entry tier and 30 to 40 one tier up, Nathan Chen says anywhere from 1 to 5 hours, William Lin says roughly as long as you would have in a real contest.

What does their disagreement actually resolve to?