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OT Analog clock math problems

Posted By: Daniel Murphy
Date: Tuesday, 4 May 2010, at 2:19 a.m.

In Response To: OT Analog clock math problems (Jason Lee)

There are 360 degrees in a circle, or clock face. When the hour hand moves one degree the minute hand moves 12. If the day begins at 12 noon, we find the first 90 degree angle by solving for

M = 12*H and M = H + 90

where M is the degrees the minute hand has moved and H is the degrees the hour hand has moved.

12*H = H+90
11*H = 90
H = 8.1818181818181818181818181818182
12*H = 98.181818181818181818181818181818

Solve for 98.181818/360 = X/60

98.181818181818181818181818181818 / 6 = 16.363636363636363636363636363636

So, the first right angle occurs at 12:16.36

Every 16.36 minutes the hands will form 90 180 270 and 360 angles. Since 270 is 360-90, at half these times the hands will be at right angles.

There are 24*60 = 1440 minutes in a day. 1440 / 16.3636 = 88.

So the answer to Jason's first question is

44.

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