Math Puzzle - A PUZZLING WATCH.

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A PUZZLING WATCH.

(Money Puzzles)
A friend pulled out his watch and said, "This watch of mine does not
keep perfect time; I must have it seen to. I have noticed that the
minute hand and the hour hand are exactly together every sixty-five
minutes." Does that watch gain or lose, and how much per hour?

Answer:

If the 65 minutes be counted on the face of the same watch, then the
problem would be impossible: for the hands must coincide every 65+5/11
minutes as shown by its face, and it matters not whether it runs fast or
slow; but if it is measured by true time, it gains 5/11 of a minute in
65 minutes, or 60/143 of a minute per hour.