document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21642>Question 21642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help with this problem! I can't seem to figure it out and my parents are of no help.\r<BR>\n" );
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document.write( "The rail line between two cities consist of two segments, one 96km longer than the other. A passenger train averages 60km/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 #10443 by </B><A HREF=/tutors/aboutme.mpl?userid=glabow><B>glabow(165)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=glabow><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What you need to know is that the time it takes to travel over a distance is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=distance+%2F+speed+=+time ALIGN=MIDDLE  ALT=\"distance+%2F+speed+=+time\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This problem has three distances that are given as a shorter distance, a longer distance that is the short distance plus 96, and the total distance which (of course) is their sum.<BR>\n" );
document.write( "Let x be the shorter distance. The time it took to travel over x was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2F+60 ALIGN=MIDDLE  ALT=\"x+%2F+60\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The time it took to travel over x + 96 was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+96%29+%2F+120 ALIGN=MIDDLE  ALT=\"+%28x+%2B+96%29+%2F+120\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The time it took to travel over the entire distance was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+x+%2B+96%29+%2F+100 ALIGN=MIDDLE  ALT=\"+%28x+%2B+x+%2B+96%29+%2F+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Of course, the time for the total distance must equal the sum of the times for each segment, so <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2F+60%29+%2B+%28%28x+%2B+96%29+%2F+120%29+=+%282x+%2B+96%29+%2F+100 ALIGN=MIDDLE  ALT=\"%28x+%2F+60%29+%2B+%28%28x+%2B+96%29+%2F+120%29+=+%282x+%2B+96%29+%2F+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You solve this for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2F+120%29+%2B+%28%28x%2B96%29%2F120%29+=+%282x%2B96%29%2F100 ALIGN=MIDDLE  ALT=\"%282x+%2F+120%29+%2B+%28%28x%2B96%29%2F120%29+=+%282x%2B96%29%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > [get common denominator]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B96%29%2F120+=+%282x%2B96%29%2F100 ALIGN=MIDDLE  ALT=\"%283x%2B96%29%2F120+=+%282x%2B96%29%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > [simplify]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300x+%2B%28100%29%2A%2896%29=240x+%2B%28120%29%2A%2896%29 ALIGN=MIDDLE  ALT=\"300x+%2B%28100%29%2A%2896%29=240x+%2B%28120%29%2A%2896%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [multiply both sides by both denominators]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60x+=+%2820%29%2A%2896%29 ALIGN=MIDDLE  ALT=\"60x+=+%2820%29%2A%2896%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [simplify]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+96 ALIGN=MIDDLE  ALT=\"3x+=+96\"   DISABLED_style= \"max-width:90%; height:auto;\" > [divide both sides by 20]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=32 ALIGN=MIDDLE  ALT=\"x=32\"   DISABLED_style= \"max-width:90%; height:auto;\" > [divide both sides by 3]<BR>\n" );
document.write( "So, x+96= 128, and the total distance is 160.<BR>\n" );
document.write( "Check by calculating the time taken for each segment and for the total:<BR>\n" );
document.write( "32/60 = .5333333333...<BR>\n" );
document.write( "128/120 = 1.06666666...<BR>\n" );
document.write( "160/100 = 1.6<BR>\n" );
document.write( ".5333333... + 1.06666666... = 1.6 [think of it as .5 and 1/3 of a tenth plus 1.0 and 2/3 of a tenth, which is 1.5 plus a whole tenth]  </SPAN>\n" );
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