document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179311>Question 179311</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Just like my other question, I keep coming with wrong equations, these are my final assignment and I have to get it right...I need help in word problems, my weakest part is comming up with the right equation...<BR>\n" );
document.write( "Kim starts to walk 3 mi to school at<BR>\n" );
document.write( "7:30 A.M. with a temperature of 0°F. Her brother Bryan<BR>\n" );
document.write( "starts at 7:45 A.M. on his bicycle, traveling 10 mph faster<BR>\n" );
document.write( "than Kim. If they get to school at the same time, then how<BR>\n" );
document.write( "fast is each one traveling? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134216 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=134216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we know the distance are equal 3 miles<BR>\n" );
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document.write( "lets call kims rate r and her time t<BR>\n" );
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document.write( "Bryan's r would be r+10 and his time would be t+1/4(remember this is all in hours)<BR>\n" );
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document.write( "Kim:::: 3=rt................eq 1<BR>\n" );
document.write( "Bryan:: 3=(r+10)(t-(1/4))...eq 2<BR>\n" );
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document.write( "lets rewrite eq 1 to t=3/r and plug it into eq 2<BR>\n" );
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document.write( "3=(r+10)((3/r)-(1/4))<BR>\n" );
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document.write( "3=(r+10)((12-r)/4r)found common denominator 2nd term on the right<BR>\n" );
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document.write( "12r=(r+10)(12-r)....multiplied both sides by 4r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12r=12r-r%5E2%2B120-10r ALIGN=MIDDLE  ALT=\"12r=12r-r%5E2%2B120-10r\"   DISABLED_style= \"max-width:90%; height:auto;\" >multiplied out right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2B10r-120=0 ALIGN=MIDDLE  ALT=\"r%5E2%2B10r-120=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >put all terms on one side<BR>\n" );
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document.write( "r=7.04mph-Kim's rate, (as the negative value is thrown out)<BR>\n" );
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document.write( "r+10=17.04mph-Bryans rate<BR>\n" );
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=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2%2Bbr%2Bc=0 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bbr%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1r%5E2%2B10r%2B-120+=+0 ALIGN=MIDDLE  ALT=\"1r%5E2%2B10r%2B-120+=+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=r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"r%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=%2810%29%5E2-4%2A1%2A-120=580 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2810%29%5E2-4%2A1%2A-120=580\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=580 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+=+%28-10%2B-sqrt%28+580+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-10%2B-sqrt%28+580+%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=r%5B1%5D+=+%28-%2810%29%2Bsqrt%28+580+%29%29%2F2%5C1+=+7.0415945787923 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+%28-%2810%29%2Bsqrt%28+580+%29%29%2F2%5C1+=+7.0415945787923\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+%28-%2810%29-sqrt%28+580+%29%29%2F2%5C1+=+-17.0415945787923 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+%28-%2810%29-sqrt%28+580+%29%29%2F2%5C1+=+-17.0415945787923\"   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=1r%5E2%2B10r%2B-120 ALIGN=MIDDLE  ALT=\"1r%5E2%2B10r%2B-120\"   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=1r%5E2%2B10r%2B-120+=+1%28r-7.0415945787923%29%2A%28r--17.0415945787923%29 ALIGN=MIDDLE  ALT=\"1r%5E2%2B10r%2B-120+=+1%28r-7.0415945787923%29%2A%28r--17.0415945787923%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 7.0415945787923, -17.0415945787923.\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+1%2Ax%5E2%2B10%2Ax%2B-120+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-120+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );