Final answer:
To find the true time when a fast-running clock indicates 1 p.m. on the 6th day, we calculate the total time gained by the clock and subtract it from the indicated time. The clock gains 132 minutes over the period, so the true time is 10:48 a.m.
Step-by-step explanation:
The student's question is about a clock that gains time over a certain period. In the specific scenario provided, the clock is set correctly at 11 a.m. and then gains 12 minutes in every 12 hours. We are asked to determine the true time when the clock reads 1 p.m. on the 6th day after it was set. To solve this, we need to calculate the total time gained over the five days from 11 a.m. on the first day to 1 p.m. on the sixth day.
To perform this calculation, first, we need to figure out how many 12-hour periods there are in five days plus 2 hours (from 11 a.m. to 1 p.m.). This equals to 5 days * 2 periods per day + 1 period for the extra 2 hours, giving us a total of 11 periods.
Next, we multiply the number of periods by the time gained per period, i.e., 11 * 12 minutes, resulting in a total gain of 132 minutes. To find the true time when the clock reads 1 p.m., we subtract the gained time from the clock's current time, meaning we need to turn back 132 minutes from 1 p.m. on the 6th day.
To convert 132 minutes to hours and minutes, we divide by 60, yielding 2 hours and 12 minutes. Therefore, subtracting 2 hours and 12 minutes from 1 p.m. brings us back to 10:48 a.m. Thus, the correct answer is that the true time is 10:48 a.m. when the clock shows 1 p.m. on the 6th day.