document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620351>Question 620351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket is divided into three sections: the payload and navigation section in the top, the fuel section in the middle, and the rocket engine section in the bottom. The top section is one-sixth the length of the bottom section. The middle section is one-half the length of the bottom section. The total length is 240 ft. Find the length of each section? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390082 by </B><A HREF=/tutors/aboutme.mpl?userid=dragonwalker><B>dragonwalker(73)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dragonwalker><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=390082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Both lengths are being compared to the bottom section so let us call this length 'x'\r<BR>\n" );
document.write( "\n" );
document.write( "So the total length will be the top, middle and bottom sections added together.\r<BR>\n" );
document.write( "\n" );
document.write( "The top section is 1/6th the bottom section so can be written 1/6 times x or x/6<BR>\n" );
document.write( "The middle section is 1/2 of the bottom section so we can write this x/2\r<BR>\n" );
document.write( "\n" );
document.write( "So we add them together as so: x/6 + x/2 + x\r<BR>\n" );
document.write( "\n" );
document.write( "We can simplify this by making all the denominators of the fractions the same. The easiest way is to make the denominator of x/2 into 6. We do this by multiplying the top and bottom by 3 so: x/2 becomes 3x/6.\r<BR>\n" );
document.write( "\n" );
document.write( "To make the denominator of x into a 6 we have to multiply the top and bottom by 6 as so:<BR>\n" );
document.write( "6x/6\r<BR>\n" );
document.write( "\n" );
document.write( "Now we can add the fractions together: x/6 + 3x/6 + 6x/6= 10x/6\r<BR>\n" );
document.write( "\n" );
document.write( "We know that this total length equals 240 ft so:\r<BR>\n" );
document.write( "\n" );
document.write( "10x/6 = 240\r<BR>\n" );
document.write( "\n" );
document.write( "to remove the denominator we need to multiply both sides by 6:\r<BR>\n" );
document.write( "\n" );
document.write( "6(10x)/6 = 240(6) the 6's on the left cancel each other out so:<BR>\n" );
document.write( "10x = 1440\r<BR>\n" );
document.write( "\n" );
document.write( "so to find x we can then divide both sides by 10:\r<BR>\n" );
document.write( "\n" );
document.write( "10x/10 = 1440/10<BR>\n" );
document.write( "x = 144\r<BR>\n" );
document.write( "\n" );
document.write( "So the length of the bottom section is 144 ft\r<BR>\n" );
document.write( "\n" );
document.write( "The length of the top is 1/6 x = 1/6 x 144<BR>\n" );
document.write( "= 24\r<BR>\n" );
document.write( "\n" );
document.write( "The length of the middle piece is half 144 = 144/2<BR>\n" );
document.write( "=72\r<BR>\n" );
document.write( "\n" );
document.write( "So to check let us add them together:\r<BR>\n" );
document.write( "\n" );
document.write( "72 + 24 + 144 = 240 !!!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );