### Instruction: It is currently $3\!:\!00\!:\!00 \text{ p.m.}$ What time will it be in $6666$ seconds?  (Enter the time in the format "HH:MM:SS", without including "am" or "pm".).### Response: To find the time after $6666$ seconds, I need to convert seconds into hours, minutes, and seconds.
I can use division and modulo operations to do this.
First, I divide $6666$ by $3600$, the number of seconds in an hour, to get the number of full hours elapsed.
This gives me $1$ with a remainder of $3066$.
Then, I divide the remainder $3066$ by $60$, the number of seconds in a minute, to get the number of full minutes elapsed.
This gives me $51$ with a remainder of $6$.
Finally, the remainder $6$ is the number of seconds elapsed.
So, $6666$ seconds is equivalent to $1$ hour, $51$ minutes, and $6$ seconds.
To find the new time, I need to add this amount to the current time of $3\!:\!00\!:\!00 \text{ p.m.
}$
Adding $1$ hour to $3\!:\!00\!:\!00 \text{ p.m.
}$ gives me $4\!:\!00\!:\!00 \text{ p.m.
}$
Adding $51$ minutes to $4\!:\!00\!:\!00 \text{ p.m.
}$ gives me $4\!:\!51\!:\!00 \text{ p.m.
}$
Adding $6$ seconds to $4\!:\!51\!:\!00 \text{ p.m.
}$ gives me $4\!:\!51\!:\!06 \text{ p.m.
}$