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 #141244 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=141244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The minute hand and the hour hand are each going in<BR>\n" );
document.write( "a circle at a certain speed in degrees/hr<BR>\n" );
document.write( "Between 2 and 3 o'clock, the hour hand covers 5 minutes<BR>\n" );
document.write( "of the 60 minutes on the clock face<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F60+=+1%2F12 ALIGN=MIDDLE  ALT=\"5%2F60+=+1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so if the whole face is 360 degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F12%29%2A360+=+30 ALIGN=MIDDLE  ALT=\"%281%2F12%29%2A360+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "When the hour hand moves 30 degrees, the minute and <BR>\n" );
document.write( "goes all the way around, or 360 degrees. That's 12 times<BR>\n" );
document.write( "faster than the hour hand<BR>\n" );
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document.write( "To solve the problem, I ask the question:<BR>\n" );
document.write( "If the hour hand moves a certain number of degrees be<BR>\n" );
document.write( "tween 2 and 3, what time is it when the minute hand  is<BR>\n" );
document.write( "at the hour hand's position + 180 degrees? That would put<BR>\n" );
document.write( "them directly opposite eachother.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the elapsed time in hours after 2 o'clock when the hands<BR>\n" );
document.write( "are opposite eachother<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F1 ALIGN=MIDDLE  ALT=\"360%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the rate of travel of the minute hand in degrees/ hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F1 ALIGN=MIDDLE  ALT=\"30%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate of travel of the hour hand in degrees/hr<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Reading from  12 and going clockwise, the hour hand is at the 2<BR>\n" );
document.write( "which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F12+=+1%2F6 ALIGN=MIDDLE  ALT=\"2%2F12+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the 360 degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%2A360+=+60 ALIGN=MIDDLE  ALT=\"%281%2F6%29%2A360+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "So, when the hands are opposite the hour hand is at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60+%2B+%2830%2F1%29%2At ALIGN=MIDDLE  ALT=\"60+%2B+%2830%2F1%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I want the minute hand to be this position + 180 degrees.<BR>\n" );
document.write( "I also know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F1 ALIGN=MIDDLE  ALT=\"360%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >{ is the minute's hand rate of travel)<BR>\n" );
document.write( "so, I can write <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60+%2B+%2830%2F1%29%2At+%2B+180+=+%28360%2F1%29%2At ALIGN=MIDDLE  ALT=\"60+%2B+%2830%2F1%29%2At+%2B+180+=+%28360%2F1%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=330t+=+240 ALIGN=MIDDLE  ALT=\"330t+=+240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+24%2F33 ALIGN=MIDDLE  ALT=\"t+=+24%2F33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+.7273 ALIGN=MIDDLE  ALT=\"t+=+.7273\"   DISABLED_style= \"max-width:90%; height:auto;\" >hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+.7273%2A60 ALIGN=MIDDLE  ALT=\"t+=+.7273%2A60\"   DISABLED_style= \"max-width:90%; height:auto;\" >min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+43.64 ALIGN=MIDDLE  ALT=\"t+=+43.64\"   DISABLED_style= \"max-width:90%; height:auto;\" >min<BR>\n" );
document.write( "and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.64%2A60+=+38 ALIGN=MIDDLE  ALT=\".64%2A60+=+38\"   DISABLED_style= \"max-width:90%; height:auto;\" >sec<BR>\n" );
document.write( "The hands are opposite eachother at 43 min and 38 sec past 2 o'clock<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "In degrees the hour hand has moved <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.7273%2A%2830%2F1%29+=+21.82 ALIGN=MIDDLE  ALT=\".7273%2A%2830%2F1%29+=+21.82\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "In degrees, the minute hand has moved<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.7273%2A%28360%2F1%29+=+261.82 ALIGN=MIDDLE  ALT=\".7273%2A%28360%2F1%29+=+261.82\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=261.82+-+21.82+=+240 ALIGN=MIDDLE  ALT=\"261.82+-+21.82+=+240\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees<BR>\n" );
document.write( "If I subtract the 60 degree headstart the hour hand had,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240+-+60+=+180 ALIGN=MIDDLE  ALT=\"240+-+60+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </SPAN>\n" );
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