JIPMAT Clocks & Calendars — PYPs

The Setup: We need to calculate the total time elapsed and the total time gained by the faulty watch to figure out exactly when it crossed the threshold of the correct time.

Step 1: Calculate the total time and total gain
* From Tuesday 1 p.m. to Thursday 1 p.m. is exactly 48 hours.
* The watch goes from being 1 minute slow ($-1$) to 2 minutes fast ($+2$).
* Total time gained = $1 + 2 = 3$ minutes.
So, the watch gains 3 minutes every 48 hours.

Step 2: Dox the correction point
Since the watch started exactly 1 minute slow, it needs to gain exactly 1 minute to show the correct time.
* If it gains 3 minutes in 48 hours...
* It gains 1 minute in $\frac{48}{3} = 16$ hours.

Step 3: Secure the target time
We just add 16 hours to the starting time (Tuesday 1 p.m.).
* Tuesday 1 p.m. + 12 hours = Wednesday 1 a.m.
* Wednesday 1 a.m. + 4 hours = Wednesday 5 a.m.

Final Answer: 5:00 am on Wednesday