document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530172>Question 530172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a train travels 180 miles in an hour less time than a bus traveling the same distance. if the speed of the bus is 15 mph slower that the speed of the train, find the speed of the train and bus?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #349927 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=349927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a train travels 180 miles in an hour less time than a bus traveling the same distance.<BR>\n" );
document.write( " if the speed of the bus is 15 mph slower that the speed of the train, find the speed of the train and bus? <BR>\n" );
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document.write( "Let s = speed of the bus<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+15) = speed of the train<BR>\n" );
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document.write( "Write a time equation, time = dist/speed<BR>\n" );
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document.write( "Bus time - train time = 1 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2Fs ALIGN=MIDDLE  ALT=\"180%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F%28s%2B15%29 ALIGN=MIDDLE  ALT=\"180%2F%28s%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "multiply by s(s+15); results:<BR>\n" );
document.write( "180(s+15) - 180s = s(s+15)<BR>\n" );
document.write( "180s + 2700 - 180s = s^2 + 15s<BR>\n" );
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document.write( "a quadratic equation<BR>\n" );
document.write( "s^2 + 15s - 2700 = 0<BR>\n" );
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document.write( "Factor to<BR>\n" );
document.write( "(s+60)(s-45) = 0<BR>\n" );
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document.write( "the positive solution<BR>\n" );
document.write( "s = 45 mph is the speed of the bus<BR>\n" );
document.write( "then<BR>\n" );
document.write( "45 + 15 = 60 mph is the speed of the train<BR>\n" );
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document.write( "Check this by finding the times of each<BR>\n" );
document.write( "180/45 = 4 hrs<BR>\n" );
document.write( "180/60 = 3 hrs<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "differ:  1 hrs </SPAN>\n" );
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