document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188391>Question 188391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At what time between 2 and 3 o'clock are the hands of the clock opposite each other?\r<BR>\n" );
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document.write( "Thank you for your help..=) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141241 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=141241\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us start at 12:00 when the two hands are together.\r<BR>\n" );
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document.write( "The hour hand will pass through A degrees.\r<BR>\n" );
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document.write( "The minute hand will pass through 720 degrees (2 hours) + (180 + A) degrees to be opposite the hour hand.\r<BR>\n" );
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document.write( "Since the minute hand travels 12 times as fast as the hour hand,\r<BR>\n" );
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document.write( "12A = 720 + 180 + A\r<BR>\n" );
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document.write( "11A = 900\r<BR>\n" );
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document.write( "A = 81 +  9/11\r<BR>\n" );
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document.write( "Which is 21 +  9/11 into the third hour since the first two hours take up 60 degrees.\r<BR>\n" );
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document.write( "The hour hand will have passed through 21 +  9/11 degrees since 2 o’clock, it is twice this amount in minutes past 2 o’clock since the hour hand takes 60 minutes to pass through 30 degrees (2 minutes per degree).\r<BR>\n" );
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document.write( "Therefore the time is 43 + 7/11 minutes past 2 o’clock.\r<BR>\n" );
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document.write( "We can verify this by calculating the proportions of the hour the hands have moved through in degrees with respect to an hour.\r<BR>\n" );
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document.write( "i.e. (21 + 9/11)/30 = (180 + 60 + 21 + 9/11)/360 = 8/11\r<BR>\n" );
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document.write( "180 is to be opposite, 60 is for the two hours and 21 +  9/11 is A.\r<BR>\n" );
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document.write( "Time is 2:43:38 + 2/11 of a second.<BR>\n" );
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