document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163136>Question 1163136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rope is cut into 3 parts in the ratio 1:4:5. The longest pieces is the  cut  into 3 smaller parts in the ratio 2:4:3.As a result there are 5 ropes and shorest piece measures 2.7cm. What is the ratio of the length of the shortest rope to the length of the second longest rope?? </SPAN>\n" );
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document.write( "There are many methods for solving a problem like this, and many variations of some of those methods.  Here is how I would solve the problem informally.<br><BR>\n" );
document.write( "The first cut cuts the rope into 3 pieces in the ratio 1:4:5 (10 \"parts\").<br><BR>\n" );
document.write( "The second cut cuts the longest of those 3 parts in the ratio 2:4:3 (9 \"parts\").<br><BR>\n" );
document.write( "So rewrite the first ratio using 10*9 = 90 parts.  1:4:5 --> 9:36:45.<br><BR>\n" );
document.write( "Now divide the 45 into the ratio 2:4:3.  2:4:3 --> 10:20:15<br><BR>\n" );
document.write( "And now we have 5 pieces of rope of lengths 9, 36, 10, 20, and 15.<br><BR>\n" );
document.write( "In order of lengths, that is 9, 10, 15, 20, and 36.<br><BR>\n" );
document.write( "ANSWER: The ratio of shortest to second longest is 9:20.<br><BR>\n" );
document.write( "Note the given length of the shortest piece is irrelevant, because the question is about the ratio of the lengths of two pieces -- no about the lengths of any pieces.<br><BR>\n" );
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