To determine the time shown by the watch on Thursday when the correct time is 0500h, we first need to calculate how long it has been since the watch was set correctly at 1100h on Sunday.
Step 1: Calculate the duration from Sunday at 1100h to Thursday at 0500h.
- From Sunday at 1100h to Monday at 1100h is 24 hours.
- From Monday at 1100h to Tuesday at 1100h is another 24 hours.
- From Tuesday at 1100h to Wednesday at 1100h is another 24 hours.
- From Wednesday at 1100h to Thursday at 1100h is another 24 hours.
- Finally, from Thursday at 1100h to Thursday at 0500h is -6 hours.
Adding this all together:
\(24 + 24 + 24 + 24 - 6 = 90 \text{ hours}\)
Step 2: Calculate how much time the watch loses.
The watch loses 8 seconds every hour. Thus, over 90 hours, the total time lost is:
\[ 90 \text{ hours} \times 8 \text{ seconds/hour} = 720 \text{ seconds} \]
Step 3: Convert the lost time into hours and seconds.
\[ 720 \text{ seconds} = \frac{720}{60} \text{ minutes} = 12 \text{ minutes} \]
Step 4: Determine the time shown on the watch.
Since the correct time on Thursday is 0500h and the watch loses 12 minutes, we need to subtract 12 minutes from the correct time:
\[ 0500h - 12 \text{ minutes} = 0448h \]
Conclusion
Thus, the watch will show 0448h (or 4:48 AM) in a 12-hour system.
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