I understand your question as this: "How do I efficiently divide numbers by $2$ in sexagismal. (Base 60)"
Suppose you have $a*60+b$ as your time. In your case, $a=7$, $b=41$. To divide by two, just do it the way you normally would, but carrying is by $60$ instead of $10$. (Base $60$ instead of base $10$)
Divide $a$ by two. If it is even, no problem. If it is odd, then you "carry" a 60 over to $b$. So when dividing $7:41$, we get $3: \frac{41+60}{2}$. Then you just divide $b$ by $2$ (or $b+60$ if we had to carry).
So to divide $7:41$ by two, we get $3:50.5$. Lets try another. How about $16:56$? Well the first term is even so we just get $8:28$. What about $27:32$? Well, the first part will be $13$, we add $60$ to $32$ to get $92$, then divide this by two, so the answer is $13:46$.
You try one: What is $9:51$ divided by two? (answer at end)
I hope this was helpful,
Important Note: Notice that this works for other numbers besides just dividing by $2$. Dividing by any number in base $60$ is the same, we just carry $60$'s instead of $10$'s.
Even more generally, notice this works for any base $b$. Division base $b$ is just done by carrying $b$ instead of $10$.
Answer: $9:51$ divided by two is $4:55.5$. We divide $9$ by two, and get $4$, and carry the $60$ over to the $51$ to get $111$, which is $55.5$ after division by $2$.