document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186467>Question 1186467</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. Ram is speeding along a highway when he sees a police motorbike parked on<BR>\n" );
document.write( "the side of the road right next to him. He immediately starts slowing down,<BR>\n" );
document.write( "but the police motorbike accelerates to catch up with him. It is assumed that<BR>\n" );
document.write( "the two vehicles are going in the same direction in parallel paths.<BR>\n" );
document.write( "The distance that Ram has traveled in meters t seconds after he starts to<BR>\n" );
document.write( "slow down is given by d (t) = 150 + 75t - 1.2t². The distance that the police<BR>\n" );
document.write( "motorbike travels can be modeled by the equation d (t) = 4t² How long will<BR>\n" );
document.write( "it take for the police motorbike to catch up to Ram?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817380 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=817380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ram is speeding along a highway when he sees a police motorbike parked on<BR>\n" );
document.write( "the side of the road right next to him. He immediately starts slowing down,<BR>\n" );
document.write( "but the police motorbike accelerates to catch up with him. It is assumed that<BR>\n" );
document.write( "the two vehicles are going in the same direction in parallel paths.<BR>\n" );
document.write( "The distance that Ram has traveled in meters t seconds after he starts to<BR>\n" );
document.write( "slow down is given by d (t) = 150 + 75t - 1.2t². The distance that the police<BR>\n" );
document.write( "motorbike travels can be modeled by the equation d (t) = 4t² How long will<BR>\n" );
document.write( "it take for the police motorbike to catch up to Ram?<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Find t when the 2 distances are equal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150+%2B+75t+-+1.2t%5E2+=+4t%5E2 ALIGN=MIDDLE  ALT=\"150+%2B+75t+-+1.2t%5E2+=+4t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.2t%5E2+-+75t+-+150+=+0 ALIGN=MIDDLE  ALT=\"5.2t%5E2+-+75t+-+150+=+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=5.2x%5E2%2B-75x%2B-150+=+0 ALIGN=MIDDLE  ALT=\"5.2x%5E2%2B-75x%2B-150+=+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=%28-75%29%5E2-4%2A5.2%2A-150=8745 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-75%29%5E2-4%2A5.2%2A-150=8745\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=8745 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--75%2B-sqrt%28+8745+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--75%2B-sqrt%28+8745+%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-%28-75%29%2Bsqrt%28+8745+%29%29%2F2%5C5.2+=+16.2033369928893 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-75%29%2Bsqrt%28+8745+%29%29%2F2%5C5.2+=+16.2033369928893\"   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-%28-75%29-sqrt%28+8745+%29%29%2F2%5C5.2+=+-1.78026006981234 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-75%29-sqrt%28+8745+%29%29%2F2%5C5.2+=+-1.78026006981234\"   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=5.2x%5E2%2B-75x%2B-150 ALIGN=MIDDLE  ALT=\"5.2x%5E2%2B-75x%2B-150\"   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=5.2x%5E2%2B-75x%2B-150+=+%28x-16.2033369928893%29%2A%28x--1.78026006981234%29 ALIGN=MIDDLE  ALT=\"5.2x%5E2%2B-75x%2B-150+=+%28x-16.2033369928893%29%2A%28x--1.78026006981234%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 16.2033369928893, -1.78026006981234.\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+5.2%2Ax%5E2%2B-75%2Ax%2B-150+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5.2%2Ax%5E2%2B-75%2Ax%2B-150+%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 solution.<BR>\n" );
document.write( "t =~ 16.20334 seconds<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );