Question

What time after 3 o’clock will the hands of the clock be

together for the first time?

Answer 1

$minute\ hand\ ∶1\ hour\ =\ 60\ minutes\ =\ 360^\circ$

$hour\ hand:1\ hour=360/12=30^\circ$

$x/60\ast360=90+x/60\ast30$

$6x=0.5x+90^\circ$

$x=90/5.5=16.36\ minutes$

$3:16:22$