Question 1163136: 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??
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
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.
The first cut cuts the rope into 3 pieces in the ratio 1:4:5 (10 "parts").
The second cut cuts the longest of those 3 parts in the ratio 2:4:3 (9 "parts").
So rewrite the first ratio using 10*9 = 90 parts. 1:4:5 --> 9:36:45.
Now divide the 45 into the ratio 2:4:3. 2:4:3 --> 10:20:15
And now we have 5 pieces of rope of lengths 9, 36, 10, 20, and 15.
In order of lengths, that is 9, 10, 15, 20, and 36.
ANSWER: The ratio of shortest to second longest is 9:20.
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.
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
When something is divided into 3 parts in the ratio a:b:c the respective
3 parts are these 3 fractions a/(a+b+c), b/(a+b+c), and c/(a+b+c) of the
whole.
The sum of the 3 parts of the ratios are 1+4+5=10 and 2+4+3=9. Their LCM is
90, so let's let the length of the original rope be 90x.
We cut the original rope into pieces which are 1/10, 4/10, and 5/10 of the
length 90x, which are the lengths:
9x, 36x, 45x
Then we cut the 45x piece into smaller pieces which are 2/9, 4/9, and 3/9 of
the length 45x, which are the lengths:
10x, 20x, 15x.
The shortest rope is 9x.
The second longest piece is 36x.
So the ratio is 9:36 or 1:4.
The difference between our answers is the ambiguous "2nd longest piece". I
took it to mean the 2nd longest piece before we cut up what was originally
the longest piece.
Greenestamps took it to mean the 2nd longest after the longest was cut up
and what was the 2nd longest before the longest was cut up, was no longer
the 2nd longest. I suppose he's right. But 1:4 is a nicer answer. lol
Edwin
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