48. Indistinguishable Clock Hands. A person had a clock on which it was impossible to distinguish the hour hand from the minute hand. If this clock was started at noon, when would it first be impossible to tell the exact time?

The reader should remember that in such clock puzzles, there is a convention that we are able to determine fractions of a second. With this assumption, an exact answer can be given.
48. This will first occur at 12 hours \(5 \frac{5}{143}\) minutes, which could be incorrectly interpreted (due to the identical positions of the hands) as 1 hour \(\frac{60}{143}\) minutes.