(related to Problem: A Puzzling Watch)
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 $65\frac{5}{11}$ 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 $\frac{5}{11}$ of a minute in $65$ minutes, or $\frac{60}{143}$ of a minute per hour.
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