At what time between 3 PM to 4 PM minute hand and hour hand will be opposite to each other?

Consider exactly at 3 : 00, minute hand is at position '12' and hour hand is at '3' hence angle between these two hands at 3 : 00 is 90°
Since relative speed between them is 11/2° per minute or every minute hand will travel 11/2° more than the hour hand.
Then will be opposite to each other when the minute hand will travel (90 + 180) = 270° more than the hour hand. And time taken for this is (270)/(11/2) = 540/11 or 49 1/11 minute
Hence they will be opposite to each other at 3 : 49 minute : 0.09 second