🕰️ Clock Hand Alignment 🤔

Let’s re-analyze the situation:

At 4:00, the hour hand is at 120° (4 × 30°) and the minute hand is at 0°.

For the hands to point in opposite directions, they need to form a 180° angle.

Since the hour hand moves 0.5° per minute and the minute hand moves 6° per minute, the relative speed between them is:

6°/minute – 0.5°/minute = 5.5°/minute

To form a 180° angle, the minute hand needs to move:

180° / 5.5°/minute ≈ 32.73 minutes

However, this calculation assumes the hour hand doesn’t move. Since the hour hand moves 0.5° per minute, we need to adjust the calculation:

32.73 minutes × 0.5°/minute ≈ 16.365°

Adding this to the initial hour hand position:

120° + 16.365° ≈ 136.365°

Now, we need to find the time when the minute hand is at:

136.365° + 180° = 316.365°

Since the minute hand moves 6° per minute:

316.365° / 6°/minute ≈ 52.727 minutes

However, this is more than 60 minutes. We need to find the correct time within the 4-5 o’clock range:

52.727 minutes – 60 minutes = -7.273 minutes (in the 4 o’clock hour)

Since the minute hand moves 6° per minute:

-7.273 minutes × 6°/minute ≈ -43.638°

Subtracting this from the initial hour hand position:

120° – 43.638° ≈ 76.362°

Now, we need to find the time when the minute hand is at:

76.362° + 180° = 256.362°

Since the minute hand moves 6° per minute:

256.362° / 6°/minute ≈ 42.727 minutes

Rounding to the nearest minute:

x ≈ 42.7 minutes

Adding this to 4 o’clock:

🎉 The hands of the watch will point in opposite directions at approximately 4:42.7. 🕰️