At what time between 8 and 9 o'clock do the hands of a clock coincide?

The correct answer is Option (2) → \(43\frac{7}{11}\) min past 8

In one minute the minute hand turns 6° and the hour hand 0.5°, so the minute hand gains 5.5° a minute on the hour hand. The hands coincide when the minute hand has made up the gap that lies between them at 8 o’clock.

• At 8:00 the hour hand is at the 8, \(8\times30=240^\circ\) ahead of the minute hand at the 12

• Time to gain 240°: \(\displaystyle \frac{240}{5.5}=\frac{480}{11}=43\frac{7}{11}\) minutes

• So the hands coincide at \(43\frac{7}{11}\) min past 8

Tip: Between \(h\) and \(h+1\) o’clock, the hands coincide at \(\displaystyle \frac{60h}{11}\) minutes past \(h\) (here \(\frac{60\times8}{11}=\frac{480}{11}\)), because the minute hand must gain \(30h\) degrees at 5.5° a minute.