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

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 Click here to see ALL problems on Miscellaneous Word Problems 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(15663)   (Show Source): You can put this solution on YOUR website!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