SOLUTION: A 60 foot rope is cut into four pieces, with each successive piece twice as long as the previous one. Find the length of the longest piece.

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Question 50407This question is from textbook
: A 60 foot rope is cut into four pieces, with each successive piece twice as long as the previous one. Find the length of the longest piece.This question is from textbook

Found 2 solutions by ichudov, padejr:
Answer by ichudov(499) About Me  (Show Source):
You can put this solution on YOUR website!
if length of the shortest piece is "L", then the next is 2L, the next is 4L, and the next is 8L.
L+2L+3L+4L+8L = 60
18L = 60
L+=+60%2F18+=+10%2F3
the longest piece is 8L+=+8%2A%2810%2F3%29+=+80%2F3+=+26%262%2F3.
Please verify what I did to make sure that I did not make a mistake.

Answer by padejr(3) About Me  (Show Source):
You can put this solution on YOUR website!
Let 1st cut = x ft
2nd cut = 2x ft
3rd cut = 2.2.x = 4 ft
4th cut = 2.2.2.x = 8x ft
then 1st cut + 2nd cut + 3rd cut + 4th cut = 60
substitute length of each cut in, we get
x+2x+4x+8x = 60 = 15x
Then x = 4
The longest piece = 8x = 8.4 = 32 ft