Chapter 9 - Basic Algebra - 9.8 Using Equations to Solve Application Problems - 9.8 Exercises - Page 691: 46

The length of the shorter rope is $21$ ft and the length of the longer rope is $29$ ft.

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