Math Puzzle - WHAT WAS THE TIME?

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WHAT WAS THE TIME?

(Money Puzzles)
"I say, Rackbrane, what is the time?" an acquaintance asked our friend
the professor the other day. The answer was certainly curious.
"If you add one quarter of the time from noon till now to half the time
from now till noon to-morrow, you will get the time exactly."
What was the time of day when the professor spoke?

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