### Brain Teasers

# Time Lines

A clock has 60 lines on it; one at each minute interval. Everyone knows that the hour and minute hands point to the same line at 12:00. Can you figure out what time it is for these situations?

1. The hour hand is exactly on one line, and the minute hand is exactly on the NEXT line.

2. The hour hand is exactly on one line, and the minute hand is exactly on the PREVIOUS line.

1. The hour hand is exactly on one line, and the minute hand is exactly on the NEXT line.

2. The hour hand is exactly on one line, and the minute hand is exactly on the PREVIOUS line.

### Hint

Each hour, the minute hand moves 60 intervals, while the hour hand moves 5 intervals. The hour hand is exactly on a line every 12 minutes. ( 60 / 5 = 12 )### Answer

1. The time is 2:12.2. The time is 9:48.

The hour hand is exactly on a line every 12 minutes, so we only need to look at times ending in 00, 12, 24, 36, and 48.

The hands exactly overlap at 12:00. They are 5 lines apart at 11:00 and 1:00, and farther apart at other hours.

At times ending in 12, the hands are closest at 2:12, where they are 1 line apart.

At times ending in 24, the hands are closest at 4:24, where they are 2 lines apart.

At times ending in 36, the hands are closest at 7:36, where they are 2 lines apart.

At times ending in 48, the hands are closest at 9:48, where they are 1 line apart.

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