SOLUTION: What time after 11 o'clock will the hands of the clock be at right angles for the 2nd time?

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Question 780896: What time after 11 o'clock will the hands of the clock be at right angles for the 2nd time?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
At exactly 11 o'clock. the hands are
5 minutes apart. That is +5%2F60+=+1%2F12+
of a full circle, and that is +30+ degrees
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The minute hand rotates at a rate of +360%2F60+
degrees / minute. or
+6+ degrees / minute
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The hour hand rotates at a rate of
+%28%285%2F60%29%2A360%29+%2F+60+ degrees/minute
+30%2F60+=+1%2F2+ degrees / minute
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I want to find when the differences in the positions
of the hands is +270+ degrees, which is the
2nd time that they are +90+ degrees apart
( +360+-+270+=+90+ )
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Let +t+ = time in minutes
For the minute hand:
position = ( degrees/min x minutes ) + initial difference
position = +6t+%2B+30+
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For the hour hand:
position = +%281%2F2%29%2At+
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Let the difference = +270+ degees
+%28+6t+%2B+30+%29+-+%281%2F2%29%2At+=+270+
+6t+%2B+30+-+%281%2F2%29%2At+=+270+
+5.5t+=+240+
+t+=+240+%2F+5.5+
+t+=+43.636+
+.636%2A60+=+38.2+
The hands will be 90 degrees apart for
the 2nd time in 43 min 38.2 sec
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Hope I got it- looks about right