At what moment between 4 o'clock and 5 o'clock do the hour hand and the minute hand of a correct clock point in exactly the same direction?

Let the time be m minutes past 4. The minute hand is at 6m degrees from the 12 mark and the hour hand is at 120 + 0.5m degrees. Setting them equal gives 6m − 0.5m = 120, so 5.5m = 120 and m = 240/11 = 21 9/11 minutes. The traps: 20 minutes past 4 puts the minute hand on the 4 mark but ignores that the hour hand has already crept past it; 24 minutes comes from using 5m instead of 5.5m, that is from forgetting the hour hand moves at all while the minute hand catches up.