document.write( "Question 1178090: Hamilton High School starts at 8:30 am and finishes at 3:30 pm each day. The
\n" ); document.write( "number of times the hour and minute hand form a right angle on the school
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Algebra.Com's Answer #807270 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Obviously the first time the hands form a right angle is exactly at 9:00 AM\r\n" );
document.write( "and the last time is exactly at 3:00 PM. \r\n" );
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document.write( "The minute hand makes 12 revolutions in the same amount of time that it\r\n" );
document.write( "takes the hour hand to make only 1 revolution. So the angle between the\r\n" );
document.write( "hands is always either increasing or decreasing at 12-1 = 11 revolutions per\r\n" );
document.write( "12 hours. That means that the minute hand goes around the hour hand 11 times\r\n" );
document.write( "in 12 hours.  12 hours divided by 11 is 1.0909... hours.  So the hands are\r\n" );
document.write( "together every 12/11=1.0909... hours.  That means that they are opposite\r\n" );
document.write( "each other when half that time has elapsed.  So we divide that by 2 and get\r\n" );
document.write( "that the hands form right angles every 6/11=0.5454... of an hour. From 8:30\r\n" );
document.write( "to 3:30 is 7 hours. 7 hours divided by 6/11=0.5454... is 12.8334...  That\r\n" );
document.write( "means they formed a right angle 12 times during the school day.\r\n" );
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document.write( "The 12 times the hands are at right angles (to the nearest minute) are \r\n" );
document.write( "given below.  It's fun to take an old clock or watch and set the hands to\r\n" );
document.write( "those times and observe that the hands are at right angles at each of those\r\n" );
document.write( "12 times.\r\n" );
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document.write( " 9:00  <--first time they are at right angles.  Time before is before 8:30.\r\n" );
document.write( " 9:33\r\n" );
document.write( "10:05\r\n" );
document.write( "10:38\r\n" );
document.write( "11:11\r\n" );
document.write( "11:44\r\n" );
document.write( "12:16\r\n" );
document.write( "12:49\r\n" );
document.write( " 1:22\r\n" );
document.write( " 1:55\r\n" );
document.write( " 2:27\r\n" );
document.write( " 3:00  <--last time they are at right angles.  Next time is after 3:30\r\n" );
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document.write( "Edwin
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