document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=728865>Question 728865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a train, an hour after starting, meets with an accident which detains it an hour .after which it proceed at 3/5 of its former rate arrives 3hrs after time but had the accident happened 50miles farther on the line, it would have arrived 1.5hr sooner.find the length of the journey </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446156 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=446156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A train, an hour after starting, meets with an accident which detains it an hour.<BR>\n" );
document.write( "After which it proceed at 3/5 of its former rate, arriving 3 hrs late.<BR>\n" );
document.write( "But had the accident happened 50miles farther on the line, it would have arrived 1.5hr sooner.<BR>\n" );
document.write( "Find the length of the journey<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = normal speed of the train (s also = the dist traveled the 1st hr)<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".6s = speed after the accident<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let d = distance of the journey<BR>\n" );
document.write( "and <BR>\n" );
document.write( "d/s = normal time of the journey<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation for the 1st scenario<BR>\n" );
document.write( ":<BR>\n" );
document.write( "normal speed time + stopped time + 3/5 speed time - normal time = 3 hrs<BR>\n" );
document.write( "1 + 1 + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s%29%2F%28.6s%29 ALIGN=MIDDLE  ALT=\"%28d-s%29%2F%28.6s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) - <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<BR>\n" );
document.write( "2 + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s%29%2F%28.6s%29 ALIGN=MIDDLE  ALT=\"%28d-s%29%2F%28.6s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) - <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<BR>\n" );
document.write( "multiply by .6s, resulting in:<BR>\n" );
document.write( "2(.6s) + d - s - .6d = .6s(3)<BR>\n" );
document.write( "1.2s + d - s - .6d = 1.8s<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "d - .6d = 1.8s - 1.2s + s<BR>\n" );
document.write( ".4d = 1.6s<BR>\n" );
document.write( "divide both sides by .4<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6%2F.4 ALIGN=MIDDLE  ALT=\"1.6%2F.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >s<BR>\n" );
document.write( "d = 4s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "An equation for the 2nd scenario<BR>\n" );
document.write( "\" but had the accident happened 50miles farther on the line, it would have arrived 1.5hr sooner.\"<BR>\n" );
document.write( "2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2Fs ALIGN=MIDDLE  ALT=\"50%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s-50%29%2F%28.6s%29 ALIGN=MIDDLE  ALT=\"%28d-s-50%29%2F%28.6s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) - <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 - 1.5<BR>\n" );
document.write( "2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2Fs ALIGN=MIDDLE  ALT=\"50%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-s-50%29%2F%28.6s%29 ALIGN=MIDDLE  ALT=\"%28d-s-50%29%2F%28.6s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) - <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;\" > = 1.5<BR>\n" );
document.write( "Multiply by .6s<BR>\n" );
document.write( ".6s(2) + .6(50) + d - s - 50 - .6d = .6s(1.5)<BR>\n" );
document.write( "1.2s + 30 + d - s - 50 - .6d = .9s<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "1.2s - s - .9s + d -.6d -50 + 30 = 0<BR>\n" );
document.write( "-.7s + .4d - 20 = 0<BR>\n" );
document.write( "-.7s + .4d = 20<BR>\n" );
document.write( "Replace d with 4s<BR>\n" );
document.write( "-.7s + .4(4s) = 20<BR>\n" );
document.write( "-.7s + 1.6s = 20<BR>\n" );
document.write( ".9s = 20<BR>\n" );
document.write( "s = 20/.9<BR>\n" );
document.write( "s = 22.2 mph<BR>\n" );
document.write( "then<BR>\n" );
document.write( "4(22.2) = 88.8 mi is the journey </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );