A rocket is divided into three sections: the payload and navigation section in the top, the fuel section in the middle, and the rocket engine section in the bottom. The top section is one-sixth the length of the bottom section. The middle section is one-half the length of the bottom section. The total length is 240 ft. Find the length of each section?

Top part lenght = 24 ft.

Middle part = 72 ft.

Bottom part = 144 ft.

Step-by-step explanation:

First we assign varibales to each rocket part

top part length = x;

middle part length = y;

bottom part length = z;

Then from the reading we can write the next equations:

X=1/6 Z; (1)

Y=1/2 Z; (2)

X + Y + Z = 240 (3)

Then solving, we replace x and y, in the equation (3)

1/6 z + 1/2 z + z = 240

Multiply by 6 both sides:

6/6 z + 6/2 z + 6 z = 1440

z + 3 z + 6 z = 1440

Then grouping similar terms

10 z = 1440

z = 144

Then replacing in (1) and (2)

Y=1/2 * 144=72

X=1/6*144 = 24