document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=347212>Question 347212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> it takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. the express train is 20 mph faster than the freight train. find the rate of both trains </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248419 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=248419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it takes a freight train 3 hours more to travel 200 miles than it takes an<BR>\n" );
document.write( " express train to travel 120 miles.<BR>\n" );
document.write( " the express train is 20 mph faster than the freight train.<BR>\n" );
document.write( " find the rate of both trains<BR>\n" );
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document.write( "Let s = speed of the freight<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+20) = speed of the express<BR>\n" );
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document.write( "Write a time equation, time = dist/speed<BR>\n" );
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document.write( "Freight time - express time = 3 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fs ALIGN=MIDDLE  ALT=\"200%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2F%28%28s%2B20%29%29 ALIGN=MIDDLE  ALT=\"120%2F%28%28s%2B20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
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document.write( "multiply by s(s+20), results:<BR>\n" );
document.write( "200(s+20) - 120s = 3s(s+20)<BR>\n" );
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document.write( "200s + 4000 - 120s = 3s^2 + 60s<BR>\n" );
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document.write( "80s + 4000 = 3s^2 + 60s<BR>\n" );
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document.write( "0 = 3s^2 + 60s - 80s - 4000<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "3s^2 - 20s - 4000 = 0<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(3x + 100)(s - 40) = 0<BR>\n" );
document.write( "the positive solution is what we want here:<BR>\n" );
document.write( "s = 40 mph is the freight<BR>\n" );
document.write( "then<BR>\n" );
document.write( "40 + 20 = 60 mph is the express<BR>\n" );
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document.write( "Check solution by finding the travel time of each<BR>\n" );
document.write( "200/40 = 5 hr<BR>\n" );
document.write( "120/60 = 2 hr<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "differs: 3 hr    </SPAN>\n" );
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