A watch gains 3 minutes in every 30 minutes (i.e., runs fast). It is set correctly at 5:00 am. After 6 true hours, what time will this watch show?

Introduction / Context:
A consistently fast watch accumulates extra indicated minutes. Convert a true-time interval to indicated time by adding the total gain.

Given Data / Assumptions:

• Gain = 3 minutes per 30 minutes of true time.
• True interval considered = 6 hours = 12 halves of an hour.

Concept / Approach:
Total gain over 6 hours = 12 * 3 = 36 minutes.

Step-by-Step Solution:
True 6 hours after 5:00 am → 11:00 am.Indicated = 11:00 am + 36 minutes = 11:36 am.

Verification / Alternative check:
Rate form: in 60 true minutes, gain = 6 minutes; in 360 minutes, gain = 36; same result.

Why Other Options Are Wrong:
10:54 am implies a losing watch; 11:30 or 11:42 are incorrect gains.

Common Pitfalls:
Multiplying by 6 instead of by 12 half-hours.

Final Answer:
11 : 36 am