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

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(20850) (Show Source): You can put this solution on YOUR website!
Mathematically, we can calculate the hand angles in terms of time expressed in and :
.
Since the moves degrees in minutes, it moves degrees , and of minute hand.
The make a complete revolution in hours ( minutes). So the hour hand moves of a revolution( degrees) for each hour plus of a revolution (degree) for each minute. .
So the angle of hour hand is: .
If we set to calculate the minutes hand is degrees ahead, we get:

Solving for , we get .
At o'clock (call it ) we have to wait minutes before the minute hand gets degrees ahead.

We get degrees times in hours.
so, your answer is :
c)
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