🕰️ Clock Hand Alignment 🤔

To find the time when the hands are in the same straight line but not together, we need to calculate the position of the hour and minute hands.

Let’s assume the time is 7 hours and x minutes.

Hour hand movement = 210° (7 × 30°) + 0.5x°

Minute hand movement = 6x°

Since the hands are in the same straight line but not together, they form a 180° angle.

|Hour hand movement – Minute hand movement| = 180°

Simplifying the equation:

|210° + 0.5x° – 6x°| = 180°

Combine like terms:

|-5.5x° + 210°| = 180°

Subtract 210° from both sides:

|-5.5x°| = -30°

Divide by -5.5:

x ≈ 5.45 minutes

Rounding to the nearest minute:

x ≈ 5 minutes

Adding this to 7 o’clock:

🎉 The hands of the clock will be in the same straight line but not together at approximately 7:05. 🕰️