Question

A 76 foot piece of rope is cut into three pieces where one piece is three times longer than the other two equal pieces. How long is each piece? (decimals allowed)

Answer 1

Let the length of one of the shorter pieces be
`\ell`. Then, we know that two of the pieces are that length, and the third piece is
`3 \ell`. Since these are all pieces of a rope, all we need to do to figure out the lengths is add all those together, solve for
`\ell`, and then plug that back in to the desired lengths:


`3 \ell + \ell + \ell = 76 ft.`

`5 \ell = 76 ft.`

`\ell = 15.2 ft.`

Shorter pieces:
`\ell = \bf 15.2 ft.`
Longer piece:
`3 \ell = \bf 45.6 ft.`