At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min 

50 min. spaces are gained in  $\frac{60}{55}\times 50$ min. or  $54\frac{6}{11}$ 

Required time =  $54\frac{6}{11}$ min. past 4.