SOLUTION: The current time is 12 noon CST. A. What time (CST) will it be 12,997 hours from now? B. What time (CST) will it be 25,000 hours from now?

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Question 1207553: The current time is 12 noon CST.
A. What time (CST) will it be 12,997 hours from now?
B. What time (CST) will it be 25,000 hours from now?
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

A.  12997 hours from 12 noon CST is 

     541
24)12997
   120
     99
     96
      37
      24
      13

That's 541 days and 13 hours, so it will be 13 hours after 12 noon on the 542nd
day, which will be at 1:00 AM CST.

B. 25000 hours from 12 noon CST is 

    1041
24)25000
   24
    100
     96
      40
      24
      16


That's 1041 days and 16 hours, so it will be 16 hours after 12 noon on the
1042nd day, which will be at 4:00 AM CST.

Edwin
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

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 remainder 13.

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).

The remainder 13 is all we care about.
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 = 1 AM 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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