document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=522807>Question 522807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A trip between two cites 175 miles apart take 1.5 hrs less than by bus. The average speed of the bus is 15 miles per hour less than the train.  <BR>\n" );
document.write( "Find the average speeds of the train and the bus. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347167 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=347167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A trip between two cites 175 miles apart take 1.5 hrs less than by bus.<BR>\n" );
document.write( " The average speed of the bus is 15 miles per hour less than the train.<BR>\n" );
document.write( "Find the average speeds of the train and the bus.<BR>\n" );
document.write( ":<BR>\n" );
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" );
document.write( ":<BR>\n" );
document.write( "Write a time equation, time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Train time - Bus time = 1.5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175%2Fs ALIGN=MIDDLE  ALT=\"175%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175%2F%28%28s%2B15%29%29 ALIGN=MIDDLE  ALT=\"175%2F%28%28s%2B15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.5<BR>\n" );
document.write( ";<BR>\n" );
document.write( "multiply by s(s+15)<BR>\n" );
document.write( "s(s+15)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175%2Fs ALIGN=MIDDLE  ALT=\"175%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - s(s+15)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175%2F%28%28s%2B15%29%29 ALIGN=MIDDLE  ALT=\"175%2F%28%28s%2B15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.5s(s+15)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Cancel out the denominators, results:<BR>\n" );
document.write( "175(s+15) - 175s = 1.5s^2 + 22.5s<BR>\n" );
document.write( "175s + 2625 - 175s = 1.5s^2 + 22.5s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "0 = 1.5s^2 + 22.5s - 2625<BR>\n" );
document.write( "get rid of the decimals, multiply by 2<BR>\n" );
document.write( "3s^2 + 45s - 5250 = 0<BR>\n" );
document.write( "You can use the quadratic formula here, but this will factor to:<BR>\n" );
document.write( "(3s-105)(s+50) = 0<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "3s = 105<BR>\n" );
document.write( "s = 105/3<BR>\n" );
document.write( "s = 35 mph is the speed of the bus,<BR>\n" );
document.write( "then<BR>\n" );
document.write( "35+15 = 50 mph is the speed of the train<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this by finding the actual time of each<BR>\n" );
document.write( "175/35 = 5.0 hrs<BR>\n" );
document.write( "175/50 = 3.5 hrs<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "differs: 1.5 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );