At what time between 9 and 10 o'clock will the hands of a watch be together?

Explanation:-

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.
45 min. spaces are gained in $$\eqalign{ & \left( {\frac{{60}}{{55}} \times 45} \right){\text{min}}{\text{.}}\,{\text{or}}\,49\frac{1}{{11}}\,{\text{min}}. \cr & \therefore {\text{The}}\,{\text{hands}}\,{\text{are}}\,{\text{together}}\,{\text{at}}\,49\frac{1}{{11}}{\text{min}}{\text{.}}\,{\text{past}}\,9 \cr}$$