document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146811>Question 146811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #13.   A car traveling east at 45 miles per hour passes a certain intersection at 3 pm. Another car traveling north at 60 miles per hour passes the same intersection 25 minutes later. To the nearest minute, figure out when the cars are exactly 40 miles apart. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107247 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When the 2nd car reaches the intersection the 1st car is 45*25/60=18.75 miles east of it.<BR>\n" );
document.write( "We have a right triangle with the hypotenuse=40<BR>\n" );
document.write( "d=st d=distance s=speed, t=time<BR>\n" );
document.write( "Let a=60t <BR>\n" );
document.write( "b=45t+18.75, c=40<BR>\n" );
document.write( "a^2+b^2=c^2<BR>\n" );
document.write( "60t^2+(45t+18.75)^2=40^2<BR>\n" );
document.write( "3600t^2+2025t^2+1687.5t+351.56=1600<BR>\n" );
document.write( "5625t^2+1687.5t-1248.44=0<BR>\n" );
document.write( "t=.344414 hr<BR>\n" );
document.write( "=21 min (approx)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed<BR>\n" );
document.write( ".<BR>\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=5625x%5E2%2B1687.5x%2B-1248.44+=+0 ALIGN=MIDDLE  ALT=\"5625x%5E2%2B1687.5x%2B-1248.44+=+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=%281687.5%29%5E2-4%2A5625%2A-1248.44=30937556.25 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%281687.5%29%5E2-4%2A5625%2A-1248.44=30937556.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=30937556.25 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+=+%28-1687.5%2B-sqrt%28+30937556.25+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-1687.5%2B-sqrt%28+30937556.25+%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-%281687.5%29%2Bsqrt%28+30937556.25+%29%29%2F2%5C5625+=+0.344413681939415 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%281687.5%29%2Bsqrt%28+30937556.25+%29%29%2F2%5C5625+=+0.344413681939415\"   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-%281687.5%29-sqrt%28+30937556.25+%29%29%2F2%5C5625+=+-0.644413681939415 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%281687.5%29-sqrt%28+30937556.25+%29%29%2F2%5C5625+=+-0.644413681939415\"   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=5625x%5E2%2B1687.5x%2B-1248.44 ALIGN=MIDDLE  ALT=\"5625x%5E2%2B1687.5x%2B-1248.44\"   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=5625x%5E2%2B1687.5x%2B-1248.44+=+%28x-0.344413681939415%29%2A%28x--0.644413681939415%29 ALIGN=MIDDLE  ALT=\"5625x%5E2%2B1687.5x%2B-1248.44+=+%28x-0.344413681939415%29%2A%28x--0.644413681939415%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.344413681939415, -0.644413681939415.\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+5625%2Ax%5E2%2B1687.5%2Ax%2B-1248.44+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5625%2Ax%5E2%2B1687.5%2Ax%2B-1248.44+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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