Henry Ernest Dudeney/Modern Puzzles/25 - A Dreamland Clock

Modern Puzzles by Henry Ernest Dudeney: $25$

A Dreamland Clock

In a dream, I was travelling in a country where they had strange ways of doing things.

One little incident was fresh in my memory when I awakened.

I saw a clock and announced the time as it appeared to be indicated.

but my guide corrected me.

He said, "You are apparently not aware that the minute hand always moves in the opposite direction to the hour hand.

Except for this improvement, our clocks are precisely the same as those you have been accustomed to."

Now, as the hands were exactly together between the hours of $4$ and $5$ o'clock,

and they started together at noon,

what was the real time?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Clock Puzzles: $25$. -- A Dreamland Clock
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Clock Puzzles: $46$. A Dreamland Clock