🕰️ Let’s Break Down the Problem Step by Step:

Step 1: Calculate the Speed of the Hour Needle 🕒

The hour needle moves 360° in 12 hours. To find its speed, we divide 360° by 12 hours:

360° ÷ 12 hours = 30° per hour

Since there are 60 minutes in an hour, we divide 30° by 60:

30° ÷ 60 = 0.5° per minute

So, the hour needle moves 0.5° every minute.

Step 2: Calculate the Speed of the Minute Needle 🕒

The minute needle moves 360° in 60 minutes:

360° ÷ 60 minutes = 6° per minute

So, the minute needle moves 6° every minute.

Step 3: Calculate the Relative Speed Between the Two Needles 🔄

When the minute needle moves 6°, the hour needle moves 0.5°. To find the relative speed, we subtract the hour needle’s speed from the minute needle’s speed:

6° (minute needle) – 0.5° (hour needle) = 5.5° per minute

So, the minute needle is catching up to the hour needle at a rate of 5.5° per minute.

Step 4: Calculate the Time it Takes for the Two Needles to Coincide 🤔

At 3 o’clock, the hour needle is at 90°. The minute needle needs to catch up to the hour needle. We use the relative speed to find the time:

Time = Distance / Speed

= 90° / 5.5°/min

= approximately 16.36 minutes

Rounding down to the nearest minute, we get:

🕰️ The final answer is: 16 minutes 🎉