document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143415>Question 143415</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395352495/algebrahomeworkh>algebra: structure and method: book1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Carla can ride her bike 2 mph faster than Karen. It takes Carla 48 minutes less to travel 50 miles than it does Karen. What is Carla's rate (mph)? HELP MUCH APPRECIATED!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104371 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Karen travels 50 miles in t hours at r miles per hour.  Carla travels 50 miles in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-48%2F60=t-4%2F5 ALIGN=MIDDLE  ALT=\"t-48%2F60=t-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B2 ALIGN=MIDDLE  ALT=\"r%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles per hour.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Karen's trip is described by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=rt ALIGN=MIDDLE  ALT=\"50=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > and Carla's trip is described by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=%28r%2B2%29%28t-4%2F5%29 ALIGN=MIDDLE  ALT=\"50=%28r%2B2%29%28t-4%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the description of Karen's trip we can say:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=50%2Fr ALIGN=MIDDLE  ALT=\"t=50%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so Carla's trip can be described as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=%28r%2B2%29%28%2850%2Fr%29-4%2F5%29 ALIGN=MIDDLE  ALT=\"50=%28r%2B2%29%28%2850%2Fr%29-4%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50=%28r%2B2%29%28%28250-4r%29%2F5r%29 ALIGN=MIDDLE  ALT=\"50=%28r%2B2%29%28%28250-4r%29%2F5r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250r=%28r%2B2%29%28250-4r%29 ALIGN=MIDDLE  ALT=\"250r=%28r%2B2%29%28250-4r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply FOIL:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250r=250r-4r%5E2%2B500-8r ALIGN=MIDDLE  ALT=\"250r=250r-4r%5E2%2B500-8r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Collect terms, put in standard form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r%5E2%2B8r-500=0 ALIGN=MIDDLE  ALT=\"4r%5E2%2B8r-500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the quadratic:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2B2r-125 ALIGN=MIDDLE  ALT=\"r%5E2%2B2r-125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Either complete the square or use the quadratic formula.  You get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-1+%2B-+3sqrt%2814%29 ALIGN=MIDDLE  ALT=\"r=-1+%2B-+3sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Exclude the negative root, so Karen's rate was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%2B+3sqrt%2814%29 ALIGN=MIDDLE  ALT=\"-1+%2B+3sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph, and Carla's was 2 mph faster or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B3sqrt%2814%29 ALIGN=MIDDLE  ALT=\"1%2B3sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph </SPAN>\n" );
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