i got this assignment where i need to answer what the time is 550 minutes after 22:15 but the minutes really confuses me.
I got a similar assignment where i had to calculate the time 10000 hours after 16:00 but here i just added the 16 hours to 10000 and looked at at the time 10016 hours after 00 using the residue class [10016]_24 which got me [8]_24 .
How can i do it similar on the first assignment?? We need to use residue classes.
On
$$\begin{align} 15\, &+ 22(60) = \rm\ start\ time\ (mins)\\ +\ \ \ 10\, &+\ \ 9(60) = 550 = \rm\ increment\\ \hline =\ \ 25\, &+ \color{#c00}{31}(60)\\ \equiv\ \ 25\, &+ \ \ \color{#c00}7(60)\!\pmod{\color{#c00}{24}(60)}\\[.1em] {\rm by}\quad\ \ &\color{#c00}{31}\equiv\color{#c00}7\quad\pmod{\color{#c00}{24}} \end{align}\qquad$$
It's just $00:15$+$7:10=7:25.$