Final answer:
The true time when a clock that gains 10 minutes every 24 hours indicates 1 p.m. the following day, after being set correctly at 8 a.m., is approximately 12:50 p.m., option (b).
Step-by-step explanation:
The student asked what the true time would be when a clock that gains 10 minutes every 24 hours indicates 1 p.m. on the following day, given that it was set correctly at 8 a.m.
To solve this problem, first calculate the total time elapsed from 8 a.m. on the first day to 1 p.m. on the following day. This is a duration of 29 hours. Since the clock gains 10 minutes every 24 hours, we need to find out how much time it would gain in 29 hours. We can set up a proportion where 10 minutes is to 24 hours as x minutes is to 29 hours.
10 minutes / 24 hours = x minutes / 29 hours
Multiplying cross the proportion gives us:
10 minutes * 29 hours = 24 hours * x minutes
Simplifying, we find that x = (10 * 29) / 24 ≈ 12.0833 minutes.
Since the clock is gaining time, we need to subtract this gain to find the true time. Thus, at 1 p.m. according to the fast clock, the actual time would be approximately 1 p.m. minus 12 minutes, which is 12:48 p.m., but since we need to provide the answer in round figures, it's closer to 12:50 p.m.. The correct answer is (b) 12:50 p.m.