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Hands directly opposite

EasyBrainteasers~3m

At what time between 4:00 and 5:00 do a clock's hour and minute hands point in exactly opposite directions (a straight 180∘180^\circ line)? Give the number of minutes after 4:00, to two decimals.

Show hints (2)+
  1. Write each hand's angle as a function of minutes after 4:00, including the hour hand's 0.5∘0.5^\circ/min drift.
  2. Set (minute −- hour) =180∘= 180^\circ and solve; the hour hand does not stay on the 4.

Answer

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54.55 (± 0.05)

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