document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265053>Question 265053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train travels 315 miles across the plains in the same time it travels 175 miles in the mountains. If the rate of the train is 40 miles per hour slower in the mountains, find both the rate in both the plains and mountains. \r<BR>\n" );
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document.write( "That is the question, would you be able to help me organize all of this information to solve it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194968 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=194968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK<BR>\n" );
document.write( "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 of train across the plains<BR>\n" );
document.write( "Then r-40=rate of train in mountains<BR>\n" );
document.write( "Time travelling across the plains=315/r<BR>\n" );
document.write( "Time travelling in the mountains=175/(r-40)\r<BR>\n" );
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document.write( "Now we are told that the above two times are equal, so:<BR>\n" );
document.write( "315/r=175/(r-40) divide each term by 35 (just to reduce size of the numbers)<BR>\n" );
document.write( "9/r=5/(r-40) multiply each term by r(r-40) or cross multiply<BR>\n" );
document.write( "9(r-40)=5r  get rid of parens<BR>\n" );
document.write( "9r-360=5r subtract 9r from each side<BR>\n" );
document.write( "9r-9r-360=5r-9r  collect like terms<BR>\n" );
document.write( "-4r=-360<BR>\n" );
document.write( "r=90 mph---------------------rate across the plains<BR>\n" );
document.write( "r-40=90-40=50 mph -------------rate in the mountains\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "315/90=175/50<BR>\n" );
document.write( "3.5=3.5\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
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