please help

Hour hand position = 90 + min/2       (every 60 minutes the hour hand moves 30 degrees)

Minute hand = minutes x 6       (every 60 minutes the minute hand moves 360 degrees)

90 + min/2 = min x 6

180 + min = min x 12

180 + min = 12 min

180 = 11 min

16.36 = min                           3:00 + 16.36 min    = 3:16 and 21.6 sec

Ooops sorry....I went between 3 and 4 oclock!!   d'Oh !    See answers below:

0=abs((30*2) - (5.5*M)), solve for M

M =120 / 11 =10.909090...... minutes after 2 O'Clock.

60 + min/2 = min x 6

120 + min = 12min

min = 10.90

2 10 and 54.5 seconds

At what time between 2 and 3' O clock are the hand of clock together exactly ?

\(\begin{array}{|rcll|} \hline t_h &=& \dfrac{12}{11} \times 2 \\ t_h &=& 2.\overline{18}\ \text{hours} \\ &=& 2^h 10^m 54.\overline{54}^s \\ \hline \end{array} \)