At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.
55 min. are gained in 60 min
15 min. spaces are gained in 60/55 x 15 = 16 4/11 min
The hands are co-incident at 16 (4/11) past 3.
