SOLUTION: Please help me figure this out. Starting at noon, how long will it take for the hour and minute hands of a typical analog clock to form a 90 degree angle? Answers: a) 15 m

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Question 121542: Please help me figure this out.
Starting at noon, how long will it take for the hour and minute hands of a
typical analog clock to form a 90 degree angle?
Answers:
a) 15 minutes
b) 16 1/3 minutes
c) 16 4/11 minutes
d) 16 23/60 minutes
e) 16 5/12 minutes
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
Mathematically, we can calculate the hand angles in terms of time expressed in hours and minutes:
%28h%3Am%29.
Since the minute+hand moves 360+degrees in 60 minutes, it moves 6 degrees per+minute, and angle of minute hand+%28A%5Bm%5D%29+=6m.
The hour+hand make a complete revolution in 12 hours (720 minutes). So the hour hand moves 1%2F12 of a revolution(30 degrees) for each hour plus 1%2F720 of a revolution (1%2F2+degree) for each minute. .
So the angle of hour hand is: %28A%5Bh%5D%29=30h+%2B+m+%2F+2.
If we set A%5Bm%5D+=+A%5Bh%5D+%2B+90 to calculate when the minutes hand is 90 degrees ahead, we get:
+6m+=+30h+%2B+m%2F2+%2B90
Solving for m, we get m+=+%2860h%2B180%29+%2F+11.
At 12 o'clock (call it 0) we have to wait 16.36 minutes before the minute hand gets 90 degrees ahead.

We get 90 degrees 44 times in 24 hours.
so, your answer is :
c) highlight%2816+4%2F11_+minutes%29