When do the hands overlap after 8 o'clock?

Question

Solve in your head. At what exact time after 8:00 do the hour and minute hands coincide? Aim: under 30 seconds.

Accepted Answer

At 8:00 the hour hand sits at 8 	imes 30^\circ = 240^\circ, the minute hand at 0^\circ, so the hour hand leads by 240^\circ. The minute hand moves at 6^\circ/min and the hour hand at 0.5^\circ/min, so the gap closes at 5.5^\circ/min: t = \frac{240}{5.5} = \frac{480}{11} = 43	frac{7}{11} 	ext{ minutes.} Convert the fraction: 	frac{7}{11} min = 	frac{7}{11}	imes 60 = 	frac{420}{11} \approx 38.2 s. So the hands coincide at 8:43:38	frac{2}{11}. Sanity check: the hands overlap every 	frac{720}{11} \approx 65	frac{5}{11} minutes. Starting from the 7:38 overlap (the one before 8:00), addin…

When do the hands overlap after 8 o'clock?

Your answer

More Mental Math questions