document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761352>Question 761352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train travelled from Town A to Town B at a uniform speed. If the speed had been increased by 18m.p.h, the time taken for the journey would have been 3 hours less. If the speed had been reduced by 9m.p.h, the time taken for the jounry would have been 3 hours more. Find the speed of the train and the distance between Town A and Town B.\r<BR>\n" );
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document.write( "PLEASE HELP ME!!!!<BR>\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463187 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=463187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=rate (speed) of the train<BR>\n" );
document.write( "And let d=distance between the two towns<BR>\n" );
document.write( "And t=time required for the initial trip<BR>\n" );
document.write( "(r+18=speed increased by 18mph)<BR>\n" );
document.write( "(r-9=speed reduced by 9mph)<BR>\n" );
document.write( "Now we know the following:<BR>\n" );
document.write( "d=rt----------------------------eq1<BR>\n" );
document.write( "d=(r+18)(t-3)-------------------eq2<BR>\n" );
document.write( "d=(r-9)(t+3)--------------------eq3<BR>\n" );
document.write( "Looking at eq2 and 3, we see that:<BR>\n" );
document.write( "(r+18)(t-3)=(r-9)(t+3) expand each side using FOIL<BR>\n" );
document.write( "rt-3r+18t-54=rt+3r-9t-27  collect like terms<BR>\n" );
document.write( "-6r+27t=27----------------------eq1b<BR>\n" );
document.write( "Looking at eq1 and 2, we see that:<BR>\n" );
document.write( "rt=(r+18)(t-3)<BR>\n" );
document.write( "rt=rt-3r+18t-54 collect like terms<BR>\n" );
document.write( "-3r+18t=54----eq2b<BR>\n" );
document.write( "multiply eq2b by 2 and subtract eq1b from it and we get:<BR>\n" );
document.write( " (-6r+36t=108)<BR>\n" );
document.write( "-(-6r+27t=27)<BR>\n" );
document.write( "9t=81<BR>\n" );
document.write( "t=9 hrs---- time needed for the initial trip<BR>\n" );
document.write( "substitute t=9 into eq2b and we get<BR>\n" );
document.write( "-3r+18*9=54<BR>\n" );
document.write( "-3r=-108<BR>\n" );
document.write( "r=36 mph-----initial speed of the trail<BR>\n" );
document.write( "substitute r=36 mph and t=9 hr into eq1 and we get:<BR>\n" );
document.write( "d=324 mi distance between the two towns<BR>\n" );
document.write( "CK<BR>\n" );
document.write( "324=(36+18)(9-3)<BR>\n" );
document.write( "324=324<BR>\n" );
document.write( "and<BR>\n" );
document.write( "324=(36-9)(9+3)<BR>\n" );
document.write( "324=324<BR>\n" );
document.write( "OK\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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