Question

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 240ft. Find the length of each section.

Answer 1

Answer:

Let's name each of the three sections of the rocket as:

-$P$ payload and navigation

-$F$ fuel

-$E$ engine

Now, we are told that:

The top section is one-sixth the length of the bottom section:

$P=\frac{1}{6}E$    (1)

The middle section is one-half the length of the bottom section:

$F=\frac{1}{2}E$   (2)

The total length is 240ft:

$P+F+E=240ft$    (3)

We may begin by substiting (1) and (2) in equation (3), in order to find the value of the engine section $E$:

$\frac{1}{6}E+\frac{1}{2}E+E=240ft$    

$E=144ft$    (4)>>>> Value of the engine section length

Then, we substitute this value of $E$ in equations (1) and (2):

$P=\frac{1}{6}144ft$  

$P=24ft$   (5)>>>> Value of the payload and navigation section length

$F=\frac{1}{2}144ft$  

$F=72ft$    (6)>>>> Value of the fuel section length