document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=634535>Question 634535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train after traveling 150 km meets with an accident and then proceeds with 3/5 of its former speed and arrives its destination 8 hours late. Had the accident occurred 360 km further, it would have reached the destination 4 hours late. What is the total distance traveled by the train? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399849 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=399849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A train after traveling 150 km meets with an accident and then proceeds<BR>\n" );
document.write( " with 3/5 of its former speed and arrives its destination 8 hours late.<BR>\n" );
document.write( " Had the accident occurred 360 km further, it would have reached the <BR>\n" );
document.write( "destination 4 hours late.<BR>\n" );
document.write( "What is the total distance traveled by the train?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = the normal speed of the train<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".6s = the speed after the accident (3/5 the normal speed)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let d = total distance<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "(d-150)km = distance traveled at the slower speed, first scenario<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(d - (150+360)) = distance traveled at the slower speed (360 km further)<BR>\n" );
document.write( "(d - 510) km<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation for the 1st scenario<BR>\n" );
document.write( "slower time - normal time = 8 hrs<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2Fs ALIGN=MIDDLE  ALT=\"150%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-150%29%2F.6s ALIGN=MIDDLE  ALT=\"%28d-150%29%2F.6s\"   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;\" > = 8<BR>\n" );
document.write( "Multiply by .6s to clear the denominators<BR>\n" );
document.write( "(.6(150) + (d-150)) - .6d = .6s(8)<BR>\n" );
document.write( "90 + d - 150 - .6d = 4.8s<BR>\n" );
document.write( ".4d - 60 = 4.8s<BR>\n" );
document.write( ".4d - 4.8s = 60<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Same with the 2nd scenario, (accident 360 km further down the road)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=510%2Fs ALIGN=MIDDLE  ALT=\"510%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-510%29%2F.6s ALIGN=MIDDLE  ALT=\"%28d-510%29%2F.6s\"   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;\" > = 4<BR>\n" );
document.write( "Multiply by .6s to clear the denominators<BR>\n" );
document.write( "(.6(510) + (d-510)) - .6d = .6s(4)<BR>\n" );
document.write( "306 + d - 510 - .6d = 2.4s<BR>\n" );
document.write( ".4d - 204 = 2.4s<BR>\n" );
document.write( ".4d - 2.4s = 204<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the speed using elimination with these two equations<BR>\n" );
document.write( ".4d - 2.4s = 204<BR>\n" );
document.write( ".4d - 4.8s =  60<BR>\n" );
document.write( "------------------subtraction eliminates d find s<BR>\n" );
document.write( "0 + 2.4s = 144<BR>\n" );
document.write( "s = 144/2.4<BR>\n" );
document.write( "s = 60 km/hr is the normal speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".6(60) = 36 km/hr is the \"after accident speed\"<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the distance using the 1st scenario equation, replace s with 60<BR>\n" );
document.write( ".4d - 4.8(60) = 60<BR>\n" );
document.write( ".4d - 288 = 60<BR>\n" );
document.write( ".4d = 60 + 288<BR>\n" );
document.write( ".4d = 348<BR>\n" );
document.write( "d = 348/.4<BR>\n" );
document.write( "d = 870 km is the total distance<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution using the 2nd scenario<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=510%2F60 ALIGN=MIDDLE  ALT=\"510%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28870-510%29%2F36 ALIGN=MIDDLE  ALT=\"%28870-510%29%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=870%2F60 ALIGN=MIDDLE  ALT=\"870%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "8.5 + 10 - 14.5 = 4 hrs, confirms our solution of d=870km </SPAN>\n" );
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