I waited for "a third of an hour"
There are many instances in Google Books of this expression which sounds very unfamiliar to me:
Crystal wanted to work on her Science project for three-quarters of an hour. She only worked for a third of an hour. Connections Maths 7, Volume 7 - Edward Duffy,Lorraine Mottershead,G. Murty
In the Niger Delta where river craft are employed for fishing and shellfish collecting field measurements show that a 5km distance takes about half an hour for a hand-paddled dug-out and a third of an hour for the Yamaha engine - The Early History of the Niger Delta - Ebiegberi Joe Alagoa,F. N. Anozie,Nwanna Nzewunwa
"Maybe no more than a third of an hour ago," replied the mage. "You think he might have found something?" Clara turned her attention fully to the matter at hand. Gambit's End - Chad Corrie
Now remember, even though we had a gross production of $900 at 1 1 :00, we must take into consideration a second visit of about a third of an hour at "no charge" plus a laboratory invoice. The Dental Consultant Looks at Insurance
After a third of an hour, the flames began to abate, and the longboat began to list badly. A hand let her painter go. All the while, the 1 6 pounders continued their vigorous fire, and the schooner's deck reeked of cordite. Henry Lunt & the spymaster - Tom McNamara
It is reasonable to count it as a third of an hour devoted to Ph.D. students, one-third to Master's students and one-third to research- fee students. In this way, it was possible to distribute teaching hours between students on different courses.Graduate School: a Study of Graduate Work at the London School of Economics
Is a third of an hour a valid current expression? or is it used just within specific contexts, scientific for instance? or is it just an archaic expression substituted by the more common 20 minutes?
Edit:
@close-voter: what is opinion based? Which of my three questions?
"A third of an hour," is not a common expression - probably because it's much easier to say, "twenty minutes." (US)
Also, the average person can divide something in half, (like, an hour) then half it again - into quarters - much more adeptly than messing around with "thirds". (It's just easier on the brain.)
Conceptualizing "a third of an hour" is too taxing, especially when compared with the easy-peasy "twenty minutes".