document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419407>Question 419407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -Applications of Quadratic Equations<BR>\n" );
document.write( "during a bicycle race, suppose that on one particular day, the racers must complete 210 mi. One Cyclist, traveling 10 mph faster than the second cyclist, covers this distance in 2.4 h less time than the second cyclist. Find the rate of the first cyclist.\r<BR>\n" );
document.write( "\n" );
document.write( "I am so confused on how to do word problems dealing with quadratic equations...<BR>\n" );
document.write( "please email me asap!<BR>\n" );
document.write( "Thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293337 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=293337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Always remember that with d = r*t problems, each thing that is<BR>\n" );
document.write( "moving must have it's own equation, and each equation must<BR>\n" );
document.write( "refer to 1 and only 1 person or thing that is moving.<BR>\n" );
document.write( "Both cyclists go the same distance: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+210+ ALIGN=MIDDLE  ALT=\"+210+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<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 for 2nd cyclist<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > = speed for the 2nd cyclist<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "1st cyclist:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+%28s+%2B+10%29%2A%28t+-+2.4%29 ALIGN=MIDDLE  ALT=\"210+=+%28s+%2B+10%29%2A%28t+-+2.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2nd cyclist:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+s%2At ALIGN=MIDDLE  ALT=\"210+=+s%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Note that there are 2 equations and 2 unknowns,<BR>\n" );
document.write( "so this is solvable.<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+%28s+%2B+10%29%2A%28t+-+2.4%29 ALIGN=MIDDLE  ALT=\"210+=+%28s+%2B+10%29%2A%28t+-+2.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+s%2At+%2B+10t+-+2.4s+-+24 ALIGN=MIDDLE  ALT=\"210+=+s%2At+%2B+10t+-+2.4s+-+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+210%2Fs ALIGN=MIDDLE  ALT=\"t+=+210%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Substituting from (2) into (1):<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+210+%2B+10%2A%28210%2Fs%29+-+2.4s+-+24 ALIGN=MIDDLE  ALT=\"210+=+210+%2B+10%2A%28210%2Fs%29+-+2.4s+-+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.4s+=+2100%2Fs+-+24+ ALIGN=MIDDLE  ALT=\"+2.4s+=+2100%2Fs+-+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.4s%5E2+=+2100+-+24s ALIGN=MIDDLE  ALT=\"+2.4s%5E2+=+2100+-+24s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.4s%5E2+%2B+24s+-+2100+=+0 ALIGN=MIDDLE  ALT=\"+2.4s%5E2+%2B+24s+-+2100+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide through by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.4 ALIGN=MIDDLE  ALT=\"2.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5E2+%2B+10s+-+875+=+0+ ALIGN=MIDDLE  ALT=\"+s%5E2+%2B+10s+-+875+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1 ALIGN=MIDDLE  ALT=\"a+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+10 ALIGN=MIDDLE  ALT=\"b+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-875 ALIGN=MIDDLE  ALT=\"c+=+-875\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+sqrt%28+10%5E2-4%2A1%2A%28-875%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+10%5E2-4%2A1%2A%28-875%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+sqrt%28+100+%2B+3500+%29%29%2F+2+ ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+100+%2B+3500+%29%29%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+sqrt%28+3600+%29%29%2F+2+ ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+3600+%29%29%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B+60%29%2F+2+ ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B+60%29%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: the negative root gives a negative answer-can't use it) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+50%2F2 ALIGN=MIDDLE  ALT=\"s+=+50%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+25 ALIGN=MIDDLE  ALT=\"s+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 1st cyclist's rate is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+%2B+10+=+25+%2B+10 ALIGN=MIDDLE  ALT=\"s+%2B+10+=+25+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+%2B+10+=+35 ALIGN=MIDDLE  ALT=\"s+%2B+10+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 1st cyclist's speed is 35 mi/hr<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+%28s+%2B+10%29%2A%28t+-+2.4%29 ALIGN=MIDDLE  ALT=\"210+=+%28s+%2B+10%29%2A%28t+-+2.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+%2825+%2B+10%29%2A%28t+-+2.4%29+ ALIGN=MIDDLE  ALT=\"210+=+%2825+%2B+10%29%2A%28t+-+2.4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+210%2F35+=+t+-+2.4+ ALIGN=MIDDLE  ALT=\"+210%2F35+=+t+-+2.4+\"   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+=+6+%2B+2.4+ ALIGN=MIDDLE  ALT=\"t+=+6+%2B+2.4+\"   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+=+8.4 ALIGN=MIDDLE  ALT=\"t+=+8.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+s%2At ALIGN=MIDDLE  ALT=\"210+=+s%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+25%2A8.4+ ALIGN=MIDDLE  ALT=\"210+=+25%2A8.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210+=+210+ ALIGN=MIDDLE  ALT=\"210+=+210+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );