Guest Posted February 28, 2009 Report Share Posted February 28, 2009 A previous clock puzzle made me think of this one: At what times of the day are the hour hand and minute hand of an analog clock exactly at 90 degrees? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 28, 2009 Report Share Posted February 28, 2009 A previous clock puzzle made me think of this one: At what times of the day are the hour hand and minute hand of an analog clock exactly at 90 degrees? maybe never? Quote Link to comment Share on other sites More sharing options...
0 HoustonHokie Posted February 28, 2009 Report Share Posted February 28, 2009 (edited) It happens every 32:43 minutes starting at 12:16:22. So, exact times are: 12:16:22 12:49:05 1:21:49 1:54:33 2:27:16 3:00:00 3:32:44 4:05:27 4:38:11 5:10:55 5:43:38 6:16:22 6:49:05 7:21:49 7:54:33 8:27:16 9:00:00 9:32:44 10:05:27 10:38:11 11:10:55 11:43:38 Edited February 28, 2009 by HoustonHokie Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 28, 2009 Report Share Posted February 28, 2009 Ohh... I read the question wrong. Thanks Houston Hookie/ Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 1, 2009 Report Share Posted March 1, 2009 1:20 2:25 3:00 3:30 4:50 4:35 5:10 5:40 6:15 6:45 7:20 7:50 8:25 8:55 9:30 10:35 11:40 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 1, 2009 Report Share Posted March 1, 2009 1:20 2:25 3:00 3:30 4:50 4:35 5:10 5:40 6:15 6:45 7:20 7:50 8:25 8:55 9:30 10:35 11:40 nevermind, didnt think this one quite through Quote Link to comment Share on other sites More sharing options...
0 HoustonHokie Posted March 1, 2009 Report Share Posted March 1, 2009 nevermind, didnt think this one quite through You're in the ballpark - just keep in mind that the hour hand moves, too... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 1, 2009 Report Share Posted March 1, 2009 (edited) A previous clock puzzle made me think of this one: At what times of the day are the hour hand and minute hand of an analog clock exactly at 90 degrees? 3 o'clock 9 o'clock the two most obvious ones... Edited March 1, 2009 by Romulus064 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 1, 2009 Report Share Posted March 1, 2009 How many times a day does that happen? 44 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 1, 2009 Report Share Posted March 1, 2009 It happens every 32:43 minutes starting at 12:16:22. So, exact times are: 12:16:22 12:49:05 1:21:49 1:54:33 2:27:16 3:00:00 3:32:44 4:05:27 4:38:11 5:10:55 5:43:38 6:16:22 6:49:05 7:21:49 7:54:33 8:27:16 9:00:00 9:32:44 10:05:27 10:38:11 11:10:55 11:43:38 Nice work! Could you show us the method you used to arrive at the 32:43 period? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 2, 2009 Report Share Posted March 2, 2009 Nice work! Could you show us the method you used to arrive at the 32:43 period? For period: Assume t is any of times that provides 900 angle. The next 900 angled time after this, the minute arm of the clock will have traveled m minutes = m.600 on the clock, the short arm will have traveled m.600/12 on the clock. The statement: m.600 - m.600/12 = travel difference. If beginning angle is 900 that next angle will be 2700. so the travel difference is 1800 then m.600 - m.600/12 = 1800 m=36/11 = 32.72 minutes= 32:43 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 2, 2009 Report Share Posted March 2, 2009 It happens 22 times in 12 hours. The spacing is 12/22 hours = 32 min 43.63636363... seconds. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 4, 2009 Report Share Posted March 4, 2009 (edited) It happens 22 times in 12 hours. The spacing is 12/22 hours = 32 min 43.63636363... seconds. 30 * (1+1/12+1/12^2+1/12^3,...) 30 * 12/(1-1/12) 32.7272....minutes Edited March 4, 2009 by G Threat Quote Link to comment Share on other sites More sharing options...
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A previous clock puzzle made me think of this one:
At what times of the day are the hour hand and minute hand of an analog clock exactly at 90 degrees?
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