Problem: It is now between and o'clock, and six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now?
Answer Choices:
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Solution:
Let x be the number of minutes after o'clock now. Then equating vertical angles (measured in minute spaces) formed by a line through and and one in the "exactly opposite" directions, we have so that . Therefore the time is now.