document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012022>Question 1012022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many minutes after 5 o’clock, will the minute hand be 16 minute spaces behind the hour hand? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627900 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> at 5 o'clock, the hour hand is at the 25 minute mark and the minute hand is at the 0 minute mark.\r<BR>\n" );
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document.write( "at 6 o'clock, the hour hand is at the 30 minute mark and the minute hand is at the 0 minute mark, or at the 60 minute mark, depending on how you want to look at it.\r<BR>\n" );
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document.write( "based on this, we can develop a formula for the hour hand versus the minute hand.\r<BR>\n" );
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document.write( "the formula is:\r<BR>\n" );
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document.write( "hour hand in terms of minutes = 25 + x/12.\r<BR>\n" );
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document.write( "minute hand in terms of minutes = x.\r<BR>\n" );
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document.write( "based on this formula, we can determine the position of the hour hand in terms of minutes.\r<BR>\n" );
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document.write( "when x = 0, the hour hand is at the 25 + 0/12 = 25 minute mark.\r<BR>\n" );
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document.write( "when x = 60, the hour hand is at the 25 + 60/12 = 30 minute mark.\r<BR>\n" );
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document.write( "this tracks with what we know, because at 5 o'clock, the hour hand is at the 25 minute mark and at 6 o'clock, the hour hand is at the 30 minute mark.\r<BR>\n" );
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document.write( "so now we want to find out at how many minutes will the hour hand be 16 minutes behind the hour hand.\r<BR>\n" );
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document.write( "our formula becomes:\r<BR>\n" );
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document.write( "25 + x/12 - x = 16\r<BR>\n" );
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document.write( "that says that the difference of the position of the hour hand in minutes minus the position of the minute hand must be equal to 16.\r<BR>\n" );
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document.write( "if we solve for x, we will find that x = 9.81818...\r<BR>\n" );
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document.write( "when x = 9.81818..., 25 + x/12 = 25 + 9.81818.../12 = 25.81818....\r<BR>\n" );
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document.write( "the difference between the hour hand in terms of minutes a and the minute hand is 25.81818... - 9.81818... = 16.\r<BR>\n" );
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document.write( "in 9.81818... minutes after 5:00 o'clock, the hour hand and the minute hand will be exactly 16 minutes apart, with the minute hand being behind the hour hand.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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