Rope Cutting

Question

A rope is 168 ft long and is to be cut into three pieces such that the second piece is 6ft less than three times the first, and the third is 2ft more than two-thirds of the second. Find the length of the longest piece.

Answer 1

d₁ = length of first piece

 

d₂ = length of second piece = 3d₁ - 6

 

d₃ = length of third piece = (2/3)d₂ + 2 = (2/3)(3d₁ - 6) + 2

 

The total length is the sum of the 3 lengths.

 

d₁ + (3d₁ - 6) + [(2/3)(3d₁ - 6) + 2] = 168

 

Solve this equation for d₁, then get d₂ and d₃, and identify the longest one.  You should be able to finish from here.