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: $3 \ell = \bf 45.6 ft.$