Question

A 120-foot-long rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope?

Answer 1

`60` ft

Explanation:

Call `x, y, z` the lengths of the 3 pieces of rope.
We get 3 equations
`x = 2y" " (1)` --> first piece x twice as long as second piece y
`z = 3y" " (2)`-> Third piece z three times as long as second piece y
`x + y + z = 120 " "(3)` --> Total length of 3 pieces

Replace `x and z` by their values from `(1) and (2)`

`(2y) + y + (3y) = 120`
`6y = 120 --> y = 20`

Then, `x = 2y = 40`, and the longest piece `z = 3y = 60`.ft

Answer 2

60 feet.

Explanation:

Choose the length of the shortest length of rope to be `x`
(t is easier to add and multiply than it is to subtract or divide.)

Write the length of each of the other pieces 'in terms of `x`'

Let the length of the second piece be `x`

The length of the first piece is `2x " (it is twice as long)"`
The length of the third piece is `3x " (it is three times as long)"`

The sum of all three pieces is `120` feet

`x +2x +3x =120`

`6x = 120`

`x = 20` feet

The longest piece is `3x = 3 xx 20 = 60` feet