If the water image of a clock shows 10:20, what is the actual time?

Concept: A water image of a clock is the reflection you would see in still water placed below the dial. This reflects the hands across the clock's horizontal (3–9) axis, which is different from a mirror image, formed by reflecting across the vertical (12–6) axis.

Because of this fixed axis, the actual time and its water image are always related by one rule: if the water-image minutes are less than 30, the actual time equals 18:30 minus the water-image time; if the water-image minutes are 30 or more, use 17:90 minus the water-image time instead (17:90 is the same instant as 18:30, written so the minutes can be subtracted without borrowing).

Application:

1. The water image shown is 10:20.

2. Its minutes, 20, are less than 30, so the actual time is found using the 18:30 reference.

3. Subtract hour from hour and minute from minute: 18 − 10 = 8 hours, and 30 − 20 = 10 minutes.

4. So the actual time on the clock is 08:10.

Cross-check:

• Reversing the rule confirms it: the water image of 08:10 is 18:30 − 08:10 = 10:20, exactly the value given in the question.

• 08:00 would follow only from a reference point ten minutes off the correct one for a water image.

• 08:50 would follow only from combining the minutes in the wrong direction while still subtracting the hours correctly.

• 09:30 would follow only from applying the reference point used for a mirror image instead of a water image.

Answer: The actual time is 08:10.