At what time between 1 and 2 O' clock are the hands of a clock together?

At 1 O' clock the the hour hand is at 1 and the minute hand is at 12.
Thus, they are 5 min spaces apart.
To be together, the minute hand must gain 5 min over the hour hand .
55 min are gained by minute hand in 60 min.
5 min will be gained by it in = (60/55 x 5 ) = 60/11 = 5⁵/₁₁ min
Hence, the hands will coincide at 5⁵/₁₁ min past 1 .