document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839479>Question 839479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to help my daughter do her homework and it has been decades since I have done some of this. We are having a problem with a distance word problem.\r<BR>\n" );
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document.write( "As a part of her training routine for basketball, Shaylee alternates between cycling and running.  She cycles at a rate of 12mph and runs at a rate of 8mph.  If she spends 5.5 hours and covers 50 miles, how much time did she spend on each exercise.\r<BR>\n" );
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document.write( "Many thanks in advance,<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505717 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=505717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance in miles she cycled<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+d+ ALIGN=MIDDLE  ALT=\"+50+-+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance in miles she ran<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 time in hours she spent cycled<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5.5+-+t+ ALIGN=MIDDLE  ALT=\"+5.5+-+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the time in hours she spent running<BR>\n" );
document.write( "--------------------------------------------<BR>\n" );
document.write( "Equation for cycling:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+12t+ ALIGN=MIDDLE  ALT=\"+d+=+12t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for running:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+d+=+8%2A%28+5.5+-+t+%29+ ALIGN=MIDDLE  ALT=\"+50+-+d+=+8%2A%28+5.5+-+t+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "This is 2 equations and 2 unknowns, so it's solvable<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+d+=+44+-+8t+ ALIGN=MIDDLE  ALT=\"+50+-+d+=+44+-+8t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+=+d+%2B+44+-+8t+ ALIGN=MIDDLE  ALT=\"+50+=+d+%2B+44+-+8t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8t+ ALIGN=MIDDLE  ALT=\"+8t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+%2B+8t+=+d+%2B+44+ ALIGN=MIDDLE  ALT=\"+50+%2B+8t+=+d+%2B+44+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+44+ ALIGN=MIDDLE  ALT=\"+44+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+8t+%2B+6+ ALIGN=MIDDLE  ALT=\"+d+=+8t+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12t+=+8t+%2B+6+ ALIGN=MIDDLE  ALT=\"+12t+=+8t+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8t+ ALIGN=MIDDLE  ALT=\"+8t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4t+=+6+ ALIGN=MIDDLE  ALT=\"+4t+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1.5+ ALIGN=MIDDLE  ALT=\"+t+=+1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5.5+-+t+=+4+ ALIGN=MIDDLE  ALT=\"+5.5+-+t+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+12t+ ALIGN=MIDDLE  ALT=\"+d+=+12t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+12%2A1.5+ ALIGN=MIDDLE  ALT=\"+d+=+12%2A1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+18+ ALIGN=MIDDLE  ALT=\"+d+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+d+=+32+ ALIGN=MIDDLE  ALT=\"+50+-+d+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "18 = the distance in miles she cycled<BR>\n" );
document.write( "32 = the distance in miles she ran<BR>\n" );
document.write( "1.5 = the time in hours she spent cycled<BR>\n" );
document.write( "4 = the time in hours she spent running<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+d+=+8%2A%28+5.5+-+t+%29+ ALIGN=MIDDLE  ALT=\"+50+-+d+=+8%2A%28+5.5+-+t+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+18+=+8%2A%28+5.5+-+1.5+%29+ ALIGN=MIDDLE  ALT=\"+50+-+18+=+8%2A%28+5.5+-+1.5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32+=+8%2A4+ ALIGN=MIDDLE  ALT=\"+32+=+8%2A4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32+=+32+ ALIGN=MIDDLE  ALT=\"+32+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+12t+ ALIGN=MIDDLE  ALT=\"+d+=+12t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+=+12%2A1.5+ ALIGN=MIDDLE  ALT=\"+18+=+12%2A1.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+=+18+ ALIGN=MIDDLE  ALT=\"+18+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );