Question 1207553
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I'll focus on part A since the two parts are very similar.


Tutor Edwin has shown the long division process where 12997/24 = 541 <font color=red>remainder 13</font>.


The quotient 541 isn't needed so we can ignore it. 
Why do we ignore it? Because after 541 full days the clock ends up back where we started (12 PM noon).


<font color=red>The remainder 13 is all we care about.</font> 
It refers to 13 extra hours after those 541 full days (i.e. 541 lots of 24 hours each).


But notice how 13 hours is 1 extra of 12 hours
12+1 = 13
Fast-forwarding the clock 13 hours from now is really just advancing the clock 1 hour but we change from AM to PM or vice versa.


Examples:
8 AM + 13 hours = 9 PM
4 PM + 13 hours = 5 AM
12 PM + 13 hours = <font color=red>1 AM</font> which is the answer to part A.


The "CST" part won't affect your scratch work since this logic applies to any time zone, but your teacher may want you to tack "CST" onto the final answer. 


For more information search out "modular arithmetic".
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