document.write( "Question 1100015: Shortly after 5 o'clock, when the minute hand and the hour hand of the clock made a 90 degree angle, Ian went out to walk the dog. On his return, after 5:30, the two hands again made a 90 degree angle. For how many minutes was Ian out with his dog? \n" ); document.write( "
Algebra.Com's Answer #714504 by Edwin McCravy(20054)\"\" \"About 
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document.write( "In 12 hours the minute hand makes 12 revolutions while the\r\n" );
document.write( "hour hand makes only 1 revolution.  So the minute hand's\r\n" );
document.write( "angular speed RELATIVE to the hour hands' angular speed is \r\n" );
document.write( "the difference between them or 12-1 = 11 revolutions per \r\n" );
document.write( "12 hours. \r\n" );
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document.write( "Therefore from noon to midnight, there are 11 periods of \r\n" );
document.write( "time between consecutive times when the hands are exactly \r\n" );
document.write( "together.  That's approximately 1 hour and 5 minutes but \r\n" );
document.write( "EXACTLY 12/11 or 1 1/ll hours. \r\n" );
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document.write( "So each of those periods of time is 12/11 hours (1 1/11 hours) \r\n" );
document.write( "in length.\r\n" );
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document.write( "At the beginning of each of those periods the hands are together.\r\n" );
document.write( "Then, after 1/4 of one of those periods later, the hands are at 90°,\r\n" );
document.write( "and, after 1/2 of one of those periods later, the hands are at 180°,\r\n" );
document.write( "and, after 3/4 of one of those periods later, the hands are at 90° \r\n" );
document.write( "again.  Then 1/4 of one of those periods later, they are back \r\n" );
document.write( "together again.\r\n" );
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document.write( "So he went to walk the dog when exactly 1/4 of one of those periods\r\n" );
document.write( "had lapsed, and returned when exactly 3/4 of that period had lapsed.\r\n" );
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document.write( "3/4 - 1/4 = 2/4 = 1/2.\r\n" );
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document.write( "So he was gone for half of one of those 12/11 hour periods or \r\n" );
document.write( "6/11 of an hour.  That's  32 8/11 minutes.\r\n" );
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document.write( "If you have any questions, ask me in the note form below and I'll\r\n" );
document.write( "get back to you by email.\r\n" );
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document.write( "Edwin
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