Math CentralQuandaries & Queries


Question from Kristin, a student:

The question I need help with is : Bobo looked at the clock at 1:25. What was the precise measure of the angle formed by the hour and minute hands of the clock? Assume that each of the clock hands moves at a constant rate continuously around the face of the clock. Thus, in any given fractional part of an hour, each hand will move that same fractional part of an hour's worth of movement.

Hi Kristin.

At 12:00, both hands are straight up. It takes twelve hours (720 minutes) for the clock to return to this position.

1:25 is 85 minutes after 12:00.

So the hour hand has travelled 85/720 of a full circle.

The minute hand has travelled 1 25/60 full circles. The 1 doesn't make any difference to the current angle, so we ignore it.

So the angle between them is the difference 25/60 - 85/720 of a full revolution (360 degrees).

Thus the calculation in degrees is just 360 x ( 25/60 - 85/720 ).

Stephen La Rocque.

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