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Answer :
Final answer:
The true time when the clock indicates 1 p.m. on the 6th day, after gaining 12 minutes every 12 hours, is 10:58 a.m. This is calculated by assessing the total gained time over the period and subtracting it from the indicated time.
Explanation:
To determine the true time when the clock indicates 1 p.m. on the 6th day, we need to take into account the rate at which the clock gains time. The clock gains 12 minutes every 12 hours, which means it gains 1 minute every hour. From 11 a.m. on the first day to 1 p.m. on the 6th day is 5 days and 2 hours, totaling 122 hours. If the clock gains 1 minute every hour, it will have gained 122 minutes in that time period.
To calculate the true time, we convert the gained time into hours and minutes: 122 minutes is 2 hours and 2 minutes (since 120 minutes is 2 hours, and the remaining 2 minutes are simply added). So when the clock indicates 1 p.m., 2 hours and 2 minutes must be subtracted to find the true time.
Subtracting 2 hours from 1 p.m. gets us to 11 a.m., and subtracting an additional 2 minutes makes it 10:58 a.m., which is the true time when the watch indicates 1 p.m. on the 6th day.
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