At what exact time between 1 o’clock and 2 o’clock are the hour and minute hands together (coincident)?

Introduction / Context:Between 1 and 2 o’clock, the hour hand begins at 30° while the minute hand starts at 0°. They meet when the minute hand gains 30° on the hour hand at a relative speed of 5.5° per minute.

Given Data / Assumptions:

• Hour hand: 0.5° per minute; Minute hand: 6° per minute.
• Initial gap at 1:00 = 30°.

Concept / Approach:Set 5.5 t = 30 to find the catch-up time t (in minutes past 1). Express as a reduced exact fraction to avoid rounding errors.

Step-by-Step Solution:

Verification / Alternative check:General overlap formula after h o’clock: t = (60/11)h minutes; for h = 1, t = 60/11 ≈ 5.4545 minutes past 1.

Why Other Options Are Wrong:55/11, 52/11, 59/11 do not satisfy the equation 5.5 t = 30.

Common Pitfalls:Confusing the right-angle timing with the coincidence timing; forgetting hour-hand motion.

Final Answer:65/11 min past 1.