SOLUTION: What time after 3 o'clock will the hands of the clock are together for the first time?

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Question 89633: What time after 3 o'clock will the hands of the clock are together for the first time?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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What time after 3 o'clock will the hands of the clock are together for the first time?
:
Let x = minute hand position when this occurs
:
Minutes hand; 60 min = 360 degrees
Hour hand; 1 hr = 360/12 = 30 degrees
:
Min: x/60 * 360 = 6x
Hr: x/60 * 30 = .5x
:
Since it's after 3, we have to add 3 * 30 = 90 degrees to the hr angle
:
hr hand position = .5x + 90
minute hand position = 6x
:
6x = .5x + 90
6x-.5x = 90
5.5x = 90
x = 90/5.5
x = 16.36 min or 3 hr 16 min 22 sec