document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884709>Question 884709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a pleasure trip, Bells drive their car a distance of 150 km at a rate of 30 kph faster than the rate they drive their boat a distance of 50 km. If the total time of the trip is 5 ½ hours, how fast do they drive each vehicle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534589 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=534589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Previously Posted<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150km%2F%28b+%2B+30kph%29+%2B+50km%2Fb+=+5.5hr ALIGN=MIDDLE  ALT=\"150km%2F%28b+%2B+30kph%29+%2B+50km%2Fb+=+5.5hr\"   DISABLED_style= \"max-width:90%; height:auto;\" > |Multiplying thru by b(b+30) so as all denominators = 1<BR>\n" );
document.write( "150b + 50(b+30) = 5.5b(b + 30)<BR>\n" );
document.write( "5.5b^2 -35b -1500 = 0  (Tossing out the negative solution for unit measure)<BR>\n" );
document.write( "b = 20kph and car is 50kph<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=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=5.5x%5E2%2B-35x%2B-1500+=+0 ALIGN=MIDDLE  ALT=\"5.5x%5E2%2B-35x%2B-1500+=+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=%28-35%29%5E2-4%2A5.5%2A-1500=34225 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-35%29%5E2-4%2A5.5%2A-1500=34225\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=34225 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--35%2B-sqrt%28+34225+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--35%2B-sqrt%28+34225+%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-%28-35%29%2Bsqrt%28+34225+%29%29%2F2%5C5.5+=+20 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+34225+%29%29%2F2%5C5.5+=+20\"   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-%28-35%29-sqrt%28+34225+%29%29%2F2%5C5.5+=+-13.6363636363636 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-35%29-sqrt%28+34225+%29%29%2F2%5C5.5+=+-13.6363636363636\"   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=5.5x%5E2%2B-35x%2B-1500 ALIGN=MIDDLE  ALT=\"5.5x%5E2%2B-35x%2B-1500\"   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=5.5x%5E2%2B-35x%2B-1500+=+5.5%28x-20%29%2A%28x--13.6363636363636%29 ALIGN=MIDDLE  ALT=\"5.5x%5E2%2B-35x%2B-1500+=+5.5%28x-20%29%2A%28x--13.6363636363636%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 20, -13.6363636363636.\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+5.5%2Ax%5E2%2B-35%2Ax%2B-1500+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5.5%2Ax%5E2%2B-35%2Ax%2B-1500+%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" );