document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171770>Question 171770</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry: Structure and Method-Book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The rail line between two cities consists of two segments, one 96 km longer than the other. A passenger train averages 60 km/h over the shorter segment, 120 km/h over the longer, and 100 km/h for the entire trip. How far apart are the cities? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127022 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=127022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The rail line between two cities consists of two segments, one 96 km longer<BR>\n" );
document.write( " than the other. A passenger train averages 60 km/h over the shorter segment,<BR>\n" );
document.write( " 120 km/h over the longer, and 100 km/h for the entire trip.<BR>\n" );
document.write( " How far apart are the cities?<BR>\n" );
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document.write( "Let d = distance of the shorter segment (traveled at 60 km/hr)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(d+96) = distance of the longer segment (traveled at 120 km/hr)<BR>\n" );
document.write( "then <BR>\n" );
document.write( "2d + 96 = total distance between the two cities (average of 100 km/hr)<BR>\n" );
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document.write( "How about writing a time equation? Time = dist/speed:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F60 ALIGN=MIDDLE  ALT=\"d%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28d%2B96%29%29%2F120 ALIGN=MIDDLE  ALT=\"%28%28d%2B96%29%29%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282d%2B96%29%29%2F100 ALIGN=MIDDLE  ALT=\"%28%282d%2B96%29%29%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply equation by 600 to get rid of the denominators; results:<BR>\n" );
document.write( "10d + 5(d+96) = 6(2d+96)<BR>\n" );
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document.write( "10d + 5d + 480 = 12d + 576<BR>\n" );
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document.write( "10d + 5d - 12d = 576 - 480<BR>\n" );
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document.write( "3d = 96<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96%2F3 ALIGN=MIDDLE  ALT=\"96%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 32 km the shorter segment<BR>\n" );
document.write( "and<BR>\n" );
document.write( "32 + 96 = 128 km the longer segment<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2(32) + 96 = 160 km the total distance<BR>\n" );
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document.write( "Check solution by finding the times<BR>\n" );
document.write( "32/60 + 128/120 = 160/100<BR>\n" );
document.write( ".5333 + 1.0667 = 1.6<BR>\n" );
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document.write( "Did this make sense to you? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );