document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957496>Question 957496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a train covers a distance of 720 km at a speed of x km/h. On the return journey, it travels at an average speed of y km/h and completes the whole journey in an hour less. if the speed during the return journey was 10 km/h more, what were the speeds in m/s? \r<BR>\n" );
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document.write( "is there a formula to use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585116 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=585116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a train covers a distance of 720 km at a speed of x km/h. On the return journey, it travels at an average speed of y km/h and completes the whole journey in an hour less. if the speed during the return journey was 10 km/h more, what were the speeds in m/s? <BR>\n" );
document.write( "distance=720km; original speed=x km/hr; return speed=y km/hr=x+10 km/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28720km%2Fx%29-1hr=720km%2F%28x%2B10%28km%2Fhr%29%29 ALIGN=MIDDLE  ALT=\"%28720km%2Fx%29-1hr=720km%2F%28x%2B10%28km%2Fhr%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply by (x)(x+10 km/hr)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28720km%29%28x%2B10%28km%2Fhr%29%29-%281hr%29%28x%29%28x%2B10%28km%2Fhr%29%29=720xkm ALIGN=MIDDLE  ALT=\"%28720km%29%28x%2B10%28km%2Fhr%29%29-%281hr%29%28x%29%28x%2B10%28km%2Fhr%29%29=720xkm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720xkm%2B7200km%5E2%2Fhr-%28x%5E2hr%2B10xkm%29=720xkm ALIGN=MIDDLE  ALT=\"720xkm%2B7200km%5E2%2Fhr-%28x%5E2hr%2B10xkm%29=720xkm\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 720xkm from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7200km%5E2%2Fhr-x%5E2hr-10xkm=0 ALIGN=MIDDLE  ALT=\"7200km%5E2%2Fhr-x%5E2hr-10xkm=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-x^2-10x+7200=0<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=-1x%5E2%2B-10x%2B7200+=+0 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-10x%2B7200+=+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%2A-1%2A7200=28900 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-10%29%5E2-4%2A-1%2A7200=28900\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=28900 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+28900+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--10%2B-sqrt%28+28900+%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+28900+%29%29%2F2%5C-1+=+-90 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+28900+%29%29%2F2%5C-1+=+-90\"   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+28900+%29%29%2F2%5C-1+=+80 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-10%29-sqrt%28+28900+%29%29%2F2%5C-1+=+80\"   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=-1x%5E2%2B-10x%2B7200 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-10x%2B7200\"   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=-1x%5E2%2B-10x%2B7200+=+-1%28x--90%29%2A%28x-80%29 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-10x%2B7200+=+-1%28x--90%29%2A%28x-80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -90, 80.\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%2B-10%2Ax%2B7200+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-10%2Ax%2B7200+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "x=80 Original speed was 80 km/hr.<BR>\n" );
document.write( "80km/hr+10km/hr=90km/hr Return speed was 90 km/hr.<BR>\n" );
document.write( "80km/hr(1000m/km)(1hr/3600sec)=22.22 m/sec Original speed was 22.22 meters per second.<BR>\n" );
document.write( "90km(1000m/1km)(1hr/3600sec)=25 m/sec Return speed was 25 meters per second.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "(720km/80km/hr)-1hr=720km/90km/hr<BR>\n" );
document.write( "9hrs-1hrs=8hrs<BR>\n" );
document.write( "8hrs=8hrs<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );