Question 765117
What time between 2 and 3 o’clock will the angle between the hands of the
 clock be bisected by the line connecting the center of the clock and
 the 3 o’clock mark?
:
let x = position of minute hand
then
{{{x/60}}}*360 = 6x is angle (12 = 0 degrees)
:
The small hand, one hour = 30 degrees; passed 2 0'clock add 60 degrees
{{{x/60}}}*30 + 60 = {{{x/2}}} + 60, the angle of the small hand
:
The angles of the hands and 90 degrees (3 o'clock) are equal
small hand to 90 degrees = long hand to 90
90 - ({{{x/2}}}+60) = 6x - 90
90 - {{{x/2}}} - 60 = 6x - 90
30 - {{{x/2}}} = 6x - 90
30 + 120 = 6x + {{{x/2}}}
120 = 6.5x
x = 120/6.5
x = 18.46 min or 18 min 27.6 seconds
:
The time 2:18:27.6 sec will satisfy this requirement