Question

John has a piece of rope. The rope is 144 inches. He cuts the rope into three different pieces. One piece is 8 inches more than the shortest piece, and the longest piece is 13 inches longer than the shortest piece. What's the length of the longest piece?

Answer 1

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