document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=567470>Question 567470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At what time between 7pm and 8pm will the minute hand be 90 degrees 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 #366550 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=366550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each hour mark on the clock is <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;\" > of<BR>\n" );
document.write( "a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+360+ ALIGN=MIDDLE  ALT=\"+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degree circle apart. That is <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( "At 7 pm, the minute hand and hour hand are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7%2A30+=+210+ ALIGN=MIDDLE  ALT=\"+7%2A30+=+210+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees apart<BR>\n" );
document.write( "The minute hand is moving at the rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+360+%2F+60+=+6+ ALIGN=MIDDLE  ALT=\"+360+%2F+60+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees/min<BR>\n" );
document.write( "The hour hand is moving at the rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30%2F60+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+30%2F60+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degree/min<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B1%5D+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the degrees that the minute hand travels until it makes<BR>\n" );
document.write( "an angle of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+ ALIGN=MIDDLE  ALT=\"+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees with the hour hand<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B2%5D+ ALIGN=MIDDLE  ALT=\"+d%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the degrees that the hour hand travels until it makes<BR>\n" );
document.write( "an angle of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+ ALIGN=MIDDLE  ALT=\"+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees with the minute hand<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;\" > = time in minutes until they are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+ ALIGN=MIDDLE  ALT=\"+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees apart<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+210+%2B+d%5B2%5D+-+d%5B1%5D+=+90+ ALIGN=MIDDLE  ALT=\"+210+%2B+d%5B2%5D+-+d%5B1%5D+=+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6t++=+d%5B1%5D+ ALIGN=MIDDLE  ALT=\"+6t++=+d%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2At+=+d%5B2%5D+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2At+=+d%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "This is 3 equations and 3 unknowns, so it's solvable<BR>\n" );
document.write( "Substitute (2) and (3) into (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+210+%2B+%281%2F2%29%2At+-+6t+=+90+ ALIGN=MIDDLE  ALT=\"+210+%2B+%281%2F2%29%2At+-+6t+=+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+420+%2B+t+-+12t+=+180+ ALIGN=MIDDLE  ALT=\"+420+%2B+t+-+12t+=+180+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-11t+=+180+-+420+ ALIGN=MIDDLE  ALT=\"+-11t+=+180+-+420+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11t+=+240+ ALIGN=MIDDLE  ALT=\"+11t+=+240+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+21.818+ ALIGN=MIDDLE  ALT=\"+t+=+21.818+\"   DISABLED_style= \"max-width:90%; height:auto;\" > min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.818%2A60+=+49.09+ ALIGN=MIDDLE  ALT=\"+.818%2A60+=+49.09+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "The hands will be 90 degrees apart at 21 min and 49 sec past 7 PM<BR>\n" );
document.write( "hope I got it </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );