document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66510>Question 66510</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1565770390/algebrahomeworkh>Advanced mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The average speed for the first 36 miles was 12mph.  The average speed for the next 45 miles was 15mph.  What should be the average speed for the next 54 miles so that the overall average speed would be 15mph? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47159 by </B><A HREF=/tutors/aboutme.mpl?userid=uma><B>uma(370)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=uma><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=47159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The average speded for 36 miles = 12mph<BR>\n" );
document.write( "Time taken = distance/time<BR>\n" );
document.write( "           = 36/12<BR>\n" );
document.write( "           = 3 hrs\r<BR>\n" );
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document.write( "The average speed for next 45 miles = 15 mph<BR>\n" );
document.write( "Time taken = distance/time<BR>\n" );
document.write( "           = 45/15<BR>\n" );
document.write( "           = 3 hrs\r<BR>\n" );
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document.write( "Let the speed for the next 54 miles = x mph<BR>\n" );
document.write( "time taken = distance/speed<BR>\n" );
document.write( "           = 54/x\r<BR>\n" );
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document.write( "Total distance = 36 + 45 + 54<BR>\n" );
document.write( "               = 135 miles\r<BR>\n" );
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document.write( "Total time = 3 + 3 + 54/x<BR>\n" );
document.write( "           = 6 + 54/x<BR>\n" );
document.write( "           = (6x + 54)/x hrs  [taking LCM and adding]\r<BR>\n" );
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document.write( "THus the average speed for the entire journey = distance /time\r<BR>\n" );
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document.write( "                                              = 135/ (6x+54)/x<BR>\n" );
document.write( "                                             = 135x/(6x+54)\r<BR>\n" );
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document.write( "Given the overall speed = 15 mph\r<BR>\n" );
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document.write( "==>  135x/(6x+54)  = 15<BR>\n" );
document.write( "==> 135x = 15(6x+54)<BR>\n" );
document.write( "==> 135x = 90x + 810<BR>\n" );
document.write( "==> 135x - 90x = 810<BR>\n" );
document.write( "==> 45x = 810<BR>\n" );
document.write( "==> x = 810/45<BR>\n" );
document.write( "==> x = 18\r<BR>\n" );
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document.write( "Thus the speed for the last 54 miles has to be 18 mph to get an overall average speed of 15 mph\r<BR>\n" );
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document.write( "Good Luck!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );