document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270675>Question 270675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train traveled the first 1/6 of the distance from station A to station B at an average speed of 90 km/h, 2/3 of the distance at an average speed of 120 km/h, and the remaining 9 km at an average speed of 90 km/h. Find the average speed at which the train was traveling from station A to station B. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198240 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=198240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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( "OK.\r<BR>\n" );
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document.write( "We know that average speed or rate: r(av)=(total distance)/(total time)<BR>\n" );
document.write( "Let d=total distance from station A to Station B\r<BR>\n" );
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document.write( "Then total time is the sum of the times listed below:<BR>\n" );
document.write( "time to travel 1/6 distance =(d/6)/90=d/540<BR>\n" );
document.write( "time to travel 2/3 or 4/6 the distance=(4d/6)/120=d/180<BR>\n" );
document.write( "time to travel the remaining 9 km=9/90=1/10\r<BR>\n" );
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document.write( "Now lets look at what we have, first:<BR>\n" );
document.write( "1/6 of the distance plus 2/3 of the distance = 5/6 of the distance leaving 1/6 of the distance remaining which we are told is 9 km<BR>\n" );
document.write( "So, if (1/6)d=9, then the total distance (d)=54 km\r<BR>\n" );
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document.write( "Therefore total time would be:<BR>\n" );
document.write( " 54/540 + 54/180 + 1/10 simplify<BR>\n" );
document.write( "1/10 + 27/90 +1/10  multiply each term by 90/90<BR>\n" );
document.write( "9/90 +27/90 +9/90=45/90=1/2 hr\r<BR>\n" );
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document.write( "So, Average Speed (rav)=54/(1/2)=108 km/hr\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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