A clock was 7 minutes behind the actual time on 3 p.m. on Wednesday and 8…

When a faulty clock gains or loses time at a constant rate, its error changes linearly with real elapsed time. If the error is E1 at time T1 and E2 at time T2, the drift rate is (E2 − E1) divided by the real time from T1 to T2.

The clock reads the correct time at the instant its cumulative error becomes zero, found by scaling the deficit at T1 by the reciprocal of that rate.

1. Real time from 3 pm Wednesday to 4 pm Friday: 24 hours (to Thursday 3 pm) + 24 hours (to Friday 3 pm) + 1 hour = 49 hours.

2. Error at the start (3 pm Wednesday) is −7 minutes (behind); error at the end (4 pm Friday) is +8 minutes (ahead), so the clock gained 8 − (−7) = 15 minutes over those 49 hours.

3. Drift rate = 15 minutes over 49 hours. To erase the initial 7-minute deficit, the time needed is 49 × 7/15 = 343/15 = 22 hours and 52 minutes (since 13/15 hour = 13 × 4 = 52 minutes).

4. Adding 22 hours 52 minutes to 3:00 pm Wednesday: +22 hours lands at 1:00 pm Thursday, and +52 minutes more gives 1:52 pm on Thursday.

Cross-check from the other end: the remaining span from this instant to 4 pm Friday is 49 − 22 hours 52 minutes = 26 hours 8 minutes; at the same 15-minutes-per-49-hours rate that is about 8 minutes of further gain, exactly the +8 minutes the clock shows at 4 pm Friday, confirming the crossing point.

So the clock shows the correct time at 1:52 pm on Thursday.