Answer
The length of the shorter rope is $21$ ft and the length of the longer rope is $29$ ft.
Work Step by Step
Let $x = $ the length of the shorter piece
$(x) + (x+8) = 50$
$2x + 8 = 50$
$2x = 42$
$x = \frac{42}{2}$
$x = 21$ ft
Let $y = $ the length of the longer piece
$y = (x + 8)$
$y = 21 + 8$
$y = 29$ ft