When two inaccurate clocks next agree: A wall clock gains 2 minutes in 12 hours; a table clock loses 2 minutes in 36 hours. Both are correct at Tuesday 12 noon. When next will they show the same time again?

Introduction / Context:
Two clocks drift at different constant rates. They will next agree (show the same reading) when the faster clock advances ahead of the slower one by an integer multiple of 12 hours (720 minutes), since clock faces wrap every 12 hours. The required real time equals “wrap amount” divided by their relative rate difference.

Given Data / Assumptions:

• Fast clock rate: +2 min per 12 h ⇒ +1/6 min/h = +0.166… min/h.
• Slow clock rate: −2 min per 36 h ⇒ −1/18 min/h ≈ −0.0555… min/h.
• Relative rate = 0.166… − (−0.0555…) = 0.2222… min/h = 2/9 min/h.

Concept / Approach:
They coincide when relative lead = 720 minutes (12 hours). Time required = 720 ÷ (2/9) = 720 × 9/2 = 3240 hours = 135 days.

Step-by-Step Solution:

Verification / Alternative check:
Because 135 is an integer number of days, the real-time clock shows 12 noon again; both faces coincide at 12 noon.

Why Other Options Are Wrong:
Other options give incorrect durations or wrong time-of-day when accounting for 3240 hours.

Common Pitfalls:
Using 24-hour wrap (1440 min) instead of 12-hour wrap (720 min) for analog faces.

Final Answer:
12 noon, after 135 days