Answer:
The longest piece is 54 inches
Explanation:
let the lengths of the ropes be x,y,z
let the length of the shortest pieces be x
A piece is 8 inches more than the shortest piece, i.e y=8+x
The longest pieces is 13 inches longer than the shortest piece, i.e z=13+ x
But the rope is 144 inches, i.e x + y + z=144----------------------(1)
substitute y=8+x and z=13+x in equation (1)
x + 8+x + 13+ x =144
We can rearrange the equation, thus;
x+x+x +8+13=144
3x + 21 =144
subtract 21 from both-side of the equation
3x+21 -21 = 144-21
3x=123
Divide both-side of the equation by 3 to get the value of 3
3x/3 = 123/3
x = 41
The longest piece is z=13 + x
=13 +41
=54
Therefore the longest piece is 54 inches