Question

A rocket is divided into 3 sections. The top section is one -sixth the length of the bottom section. The middle section is one -half the length bottom section. The total length of the rocket is 240 ft. Find the length of the top section

Answer 1

Length of top section of rocket = 24 ft

Step-by-step explanation:

We have length of top section = One -sixth the length of the bottom section

Length of middle section = One -half the length bottom section.

Let length of bottom section be x.

So length of top section
`=(1)/(6)*x=(x)/(6)`

Length of middle section
`=(1)/(2)*x=(x)/(2)`

We have total length of rocket = 240 ft

Also we have, total length
`=x+(x)/(6) +(x)/(2)\\\\= (6x)/(6)+(x)/(6) +(3x)/(6)\\\\= (10x)/(6)\\\\=(5x)/(3)`

So,
`(5x)/(3)= 240\\ \\ x=144ft`

Length of bottom section = 144 ft

Length of top section
`=(1)/(6)*144=24ft`

Length of top section of rocket = 24 ft

Answer 2

Let the bottom section has length x feet.

1. The top section is
`(1)/(6)` the length of the bottom section, then the length of the top section is
`(1)/(6)x.`

2. The middle section is
`(1)/(2)` the length bottom section, then the middle section has length
`(1)/(2)x.`

3. The total length of the rocket is

`x+(1)/(6)x+(1)/(2)x`

that is 240 feet.

Thus, you have the equation

`x+(1)/(6)x+(1)/(2)x=240.`

4. Solve it. Multiply this equation by 6:

`6x+x+3x=240\cdot 6,\\\\10x=1,440.`

Divide it by 10:

`x=144\ ft.`

The length of the bottom section is 144 feet, then the length of the top section is

`(1)/(6)x=(1)/(6)\cdot 144=24\ ft.`

Answer: The top section has length 24 feet