document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=788852>Question 788852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A and B are riding bicycles on perpendicular roads. Suppose that A is 9 km from the intersection and riding toward it at 20 kph, and B is 7 km from it and riding away from it at 25 kph. After how many hours will they be 13 km arart? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478634 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=478634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A and B are riding bicycles on perpendicular roads. Suppose that A is 9 km from the intersection and riding toward it at 20 kph, and B is 7 km from it and riding away from it at 25 kph. After how many hours will they be 13 km arart?<BR>\n" );
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document.write( "A = A's distance from the intersection<BR>\n" );
document.write( "A = 9 - 20t km (t in hours)<BR>\n" );
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document.write( "B = 7 + 25t<BR>\n" );
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document.write( "The distance between them is the hypotenuse of the right triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-20t%29%5E2+%2B+%287%2B25t%29%5E2+=+13%5E2 ALIGN=MIDDLE  ALT=\"%289-20t%29%5E2+%2B+%287%2B25t%29%5E2+=+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400t%5E2+-+360t+%2B+81+%2B+625t%5E2+%2B+350t+%2B+49+=+169 ALIGN=MIDDLE  ALT=\"400t%5E2+-+360t+%2B+81+%2B+625t%5E2+%2B+350t+%2B+49+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1025t%5E2+-+10t+-+39+=+0 ALIGN=MIDDLE  ALT=\"1025t%5E2+-+10t+-+39+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=1025x%5E2%2B-10x%2B-39+=+0 ALIGN=MIDDLE  ALT=\"1025x%5E2%2B-10x%2B-39+=+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=%28-10%29%5E2-4%2A1025%2A-39=160000 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-10%29%5E2-4%2A1025%2A-39=160000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=160000 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+160000+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--10%2B-sqrt%28+160000+%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-%28-10%29%2Bsqrt%28+160000+%29%29%2F2%5C1025+=+0.2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+160000+%29%29%2F2%5C1025+=+0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-10%29-sqrt%28+160000+%29%29%2F2%5C1025+=+-0.190243902439024 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-10%29-sqrt%28+160000+%29%29%2F2%5C1025+=+-0.190243902439024\"   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=1025x%5E2%2B-10x%2B-39 ALIGN=MIDDLE  ALT=\"1025x%5E2%2B-10x%2B-39\"   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=1025x%5E2%2B-10x%2B-39+=+%28x-0.2%29%2A%28x--0.190243902439024%29 ALIGN=MIDDLE  ALT=\"1025x%5E2%2B-10x%2B-39+=+%28x-0.2%29%2A%28x--0.190243902439024%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.2, -0.190243902439024.\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+1025%2Ax%5E2%2B-10%2Ax%2B-39+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1025%2Ax%5E2%2B-10%2Ax%2B-39+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "Ignore the negative result.<BR>\n" );
document.write( "t = 0.2 hours<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );