A clock is started at noon. By 5:10, through how many degrees has the hour hand turned?

Problem restatementFind the total rotation of the hour hand from 12:00 noon to 5:10.

Given data

• Hour hand speed = 0.5° per minute (30° per hour).
• Elapsed time from 12:00 to 5:10 = 5 hours 10 minutes = 310 minutes.

Concept/ApproachThe hour hand advances continuously. Rotation = speed × time.

Step-by-Step calculation Rotation = 0.5°/min × 310 min = 155°

Verification/AlternativeBreak into hours + minutes: in 5 hours the hand turns 5 × 30° = 150°. In 10 minutes, it turns 10 × 0.5° = 5°. Total = 150° + 5° = 155°.

Common pitfalls

• Ignoring the extra 10 minutes of hour-hand motion.

Final Answer155°