document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173690>Question 173690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a 135-mile bycycle excursion, Maria averaged 5 mph faster for the first 60 miles than she did for the last 75 miles. The entire trip took 8 hours. Find the rate for the first 60 miles. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128557 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have to set this up as 2 different parts of a lonnnnnnnnnggggggg trip.<BR>\n" );
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document.write( "lets call the 2nd part of the trips rate r and time t and <BR>\n" );
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document.write( "so then we will call the first part of the trips rate r+5 and the time 8-t(total time minus 2nd part of the trips time(t))<BR>\n" );
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document.write( "so<BR>\n" );
document.write( "75=rt......................eq 1<BR>\n" );
document.write( "60=(r+5)(8-t)..........eq 2<BR>\n" );
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document.write( "lets rewrite eq 1 to t=75/r and plug t's value into eq 2<BR>\n" );
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document.write( "60=(r+5)(8-(75/r))<BR>\n" );
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document.write( "60=(r+5)((8r-75)/r).........now multiply both sides by r<BR>\n" );
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document.write( "60r=(r+5)(8r-75)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60r=8r%5E2-75r%2B40r-375 ALIGN=MIDDLE  ALT=\"60r=8r%5E2-75r%2B40r-375\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8r%5E2-95r-375%2B0 ALIGN=MIDDLE  ALT=\"8r%5E2-95r-375%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "throw out negative answer<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r=15%2Cr=-3.125%29 ALIGN=MIDDLE  ALT=\"system%28r=15%2Cr=-3.125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "therefore rate on 75 mile part of trip is 15mph<BR>\n" );
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document.write( "rate on 60 mile part of trip is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r%2B5=15%2B5-20%29 ALIGN=MIDDLE  ALT=\"highlight%28r%2B5=15%2B5-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >mph <BR>\n" );
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document.write( " <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2%2B-95x%2B-375+=+0 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-95x%2B-375+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-95%29%5E2-4%2A8%2A-375=21025 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-95%29%5E2-4%2A8%2A-375=21025\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=21025 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--95%2B-sqrt%28+21025+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--95%2B-sqrt%28+21025+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-95%29%2Bsqrt%28+21025+%29%29%2F2%5C8+=+15 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-95%29%2Bsqrt%28+21025+%29%29%2F2%5C8+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-95%29-sqrt%28+21025+%29%29%2F2%5C8+=+-3.125 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-95%29-sqrt%28+21025+%29%29%2F2%5C8+=+-3.125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2%2B-95x%2B-375 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-95x%2B-375\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2%2B-95x%2B-375+=+%28x-15%29%2A%28x--3.125%29 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-95x%2B-375+=+%28x-15%29%2A%28x--3.125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 15, -3.125.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-95%2Ax%2B-375+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-95%2Ax%2B-375+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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