Answer:
Let's name each of the three sections of the rocket as:
-[tex]P[/tex] payload and navigation
-[tex]F[/tex] fuel
-[tex]E[/tex] engine
Now, we are told that:
The top section is one-sixth the length of the bottom section:
[tex]P=\frac{1}{6}E[/tex] (1)
The middle section is one-half the length of the bottom section:
[tex]F=\frac{1}{2}E[/tex] (2)
The total length is 240ft:
[tex]P+F+E=240ft[/tex] (3)
We may begin by substiting (1) and (2) in equation (3), in order to find the value of the engine section [tex]E[/tex]:
[tex]\frac{1}{6}E+\frac{1}{2}E+E=240ft[/tex]
[tex]E=144ft[/tex] (4)>>>> Value of the engine section length
Then, we substitute this value of [tex]E[/tex] in equations (1) and (2):
[tex]P=\frac{1}{6}144ft[/tex]
[tex]P=24ft[/tex] (5)>>>> Value of the payload and navigation section length
[tex]F=\frac{1}{2}144ft[/tex]
[tex]F=72ft[/tex] (6)>>>> Value of the fuel section length
