Hands 3 minutes apart between 5 and 6: At what time between 5 and 6 o’clock are the hands of a clock exactly 3 minute-marks apart?

Introduction / Context:
“3 minutes apart” means an angle of 3 × 6 = 18 degrees between hands. Using the standard angle formula |30H − 5.5M|, we can solve for M in the hour after 5 o’clock. Typically two instants satisfy a small separation within an hour.

Given Data / Assumptions:

• Hour between 5 and 6 ⇒ H = 5.
• Angle condition: |30H − 5.5M| = 18.

Concept / Approach:
Write |150 − 5.5M| = 18 and solve both linear cases. Convert any fractional minute to a mixed fraction as needed.

Step-by-Step Solution:

Verification / Alternative check:
At 5:24, angle = |150 − 5.5 × 24| = |150 − 132| = 18°. The second instant (≈ 5:30 6/11) also works, but if only one option matches exactly, choose that.

Why Other Options Are Wrong:
22 and 26 past 5 are not the exact solutions from the equation; “None” is false because 24 appears and is correct.

Common Pitfalls:
Confusing “minutes apart” with “minutes past” or using 5.0M instead of 5.5M for the minute contribution of the hour hand.

Final Answer:
24 minutes past 5