55. Westminster Clocks. One morning, a man was walking across Westminster Bridge, judging by the clock tower (which is often mistakenly called Big Ben, although this name refers only to the large bell; but this is by the way) between eight and nine o'clock. Returning between four and five o'clock, he noticed that the hands had switched places. At what time did the man walk across the bridge in both directions?
55. At 8:23 \(\frac{71}{143}\) min and at 4:41 \(\frac{137}{143}\) min. In clock puzzles, we assume that fractional parts of a minute can be determined on the clock.