Question

A rocket is divided into three sections. The top section is one-eighth the length of the bottom section. The middle section is one-half the length of the bottom section. The total length of the rocket is 312ft. Find the length of the top section.

Answer 1

312 ft

Explanation:

The steps are as follows :

1. The problem can be described as an equation

`x + (1)/(2)x + (1)/(8)x = 312`

2. Convert all values on the left side into their equivalent fractional values

`(8)/(8)x + (4)/(8)x + (1)/(8) x = 312`

3. Combine like terms

`(13)/(8) x = 312`

4. Multiply both sides by the reciprocal of 13/8 to isolate variable X

`concept \: \: \: ({ (8)/(13) * (13)/(8) }) = 1`

`(8)/(13) * (13)/(8)x = 312 \: * (8)/(13)`

5. Simplify

`x = 192`

6. Check answer by using it in the original equation

`(192) + (1)/(2)(192) + (1)/(8) (192) = 312`