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.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> 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.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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(507) 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