Assume that both hands of an analogue clock turn at constant rates. - Show that the minute hand turn

Question

Assume that both hands of an analogue clock turn at constant rates. - Show that the minute hand turns through 6 per minute and the hour hand through 0.5 per minute. - Find the angle between the two hands at 3.40, and the reflex angle between them. - Find, correct to the nearest second, the time between 3 o'clock and 4 o'clock when the two hands point in the same direction. - Explain why the two hands point in the same direction exactly 11 times in every 12 hours.

Accepted Answer

(a) $360^\circ\div60=6^\circ$, $30^\circ\div60=0.5^\circ$ (b) $130^\circ$; reflex $230^\circ$ (c) about 3.16 and 22 s ($16\dfrac4{11}$ min after 3) (d) the minute hand gains $360^\circ$ every $\dfrac{720}{11}$ min, which fits $11$ times into $720$ min

Angles between the hands of a clock

Angles between the hands of a clock

Solution:

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