document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=903383>Question 903383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train, after travelling for 3 hours, was detained 40 minutes. Then it proceeded at 6/5 its former rate and arrived 10 minutes late. If the delay had occurred at a point 15 kilometers farther from its destination, the train would have been only 5 minutes late. Find the rate of the train and the total distance traveled. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #548149 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=548149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let s = the normal speed of the train<BR>\n" );
document.write( "let d = total distance of the trip <BR>\n" );
document.write( ":<BR>\n" );
document.write( "A train, after travelling for 3 hours, was detained 40 minutes.<BR>\n" );
document.write( "3s = train distance up to this point<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = normal time for the trip<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Then it proceeded at 6/5 its former rate and arrived 10 minutes late.<BR>\n" );
document.write( "faster speed = 1.2s<BR>\n" );
document.write( "at this speed it cut half an hour off the normal travel time (40-10)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - (3+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28d-3s%29%29%2F%28%281.2s%29%29 ALIGN=MIDDLE  ALT=\"%28%28d-3s%29%29%2F%28%281.2s%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = .5 hrs <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 3 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28d-3s%29%29%2F%28%281.2s%29%29 ALIGN=MIDDLE  ALT=\"%28%28d-3s%29%29%2F%28%281.2s%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .5 hrs<BR>\n" );
document.write( "add 3 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28d-3s%29%29%2F%28%281.2s%29%29 ALIGN=MIDDLE  ALT=\"%28%28d-3s%29%29%2F%28%281.2s%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.5<BR>\n" );
document.write( "multiply by 1.2s, resulting in<BR>\n" );
document.write( "1.2d - d + 3s = 3.5(1.2s)<BR>\n" );
document.write( ".2d = 4.2s - 3s<BR>\n" );
document.write( ".2d = 1.2s<BR>\n" );
document.write( "d = 1.2s/.2<BR>\n" );
document.write( "d = 6s<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3s = halfway point, where the 1st delay occurred  <BR>\n" );
document.write( ":<BR>\n" );
document.write( " If the delay had occurred at a point 15 kilometers farther from its destination, the train would have been only 5 minutes late.<BR>\n" );
document.write( "This time the train gained 40-5 = 35 minutes over the original undelayed time<BR>\n" );
document.write( "35 min = 7/12 hrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the distance traveled at the faster speed this time; (3s+15)<BR>\n" );
document.write( "The distance traveled at the normal speed: (3s-15)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "time at normal speed + time at faster speed   = normal time - 35 min <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283s-15%29%2Fs ALIGN=MIDDLE  ALT=\"%283s-15%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283s%2B15%29%2F1.2s ALIGN=MIDDLE  ALT=\"%283s%2B15%29%2F1.2s\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6s%2Fs ALIGN=MIDDLE  ALT=\"6s%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply equation by 12s<BR>\n" );
document.write( "12(3s-15) + 10(3s+15) = 12(6s) - 7s<BR>\n" );
document.write( "36s - 180 + 30s + 150 = 72s - 7s<BR>\n" );
document.write( "66s - 30 = 65s<BR>\n" );
document.write( "66s - 65s = 30<BR>\n" );
document.write( "s = 30 mph is the normal  speed of the train<BR>\n" );
document.write( "Find the distance<BR>\n" );
document.write( "6(30) = 180 mi is the distance<BR>\n" );
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document.write( " </SPAN>\n" );
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