SOLUTION: 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

Question 620351: 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?
Answer by dragonwalker(73) (Show Source): You can put this solution on YOUR website!
Both lengths are being compared to the bottom section so let us call this length 'x'
So the total length will be the top, middle and bottom sections added together.
The top section is 1/6th the bottom section so can be written 1/6 times x or x/6
The middle section is 1/2 of the bottom section so we can write this x/2
So we add them together as so: x/6 + x/2 + x
We can simplify this by making all the denominators of the fractions the same. The easiest way is to make the denominator of x/2 into 6. We do this by multiplying the top and bottom by 3 so: x/2 becomes 3x/6.
To make the denominator of x into a 6 we have to multiply the top and bottom by 6 as so:
6x/6
Now we can add the fractions together: x/6 + 3x/6 + 6x/6= 10x/6
We know that this total length equals 240 ft so:
10x/6 = 240
to remove the denominator we need to multiply both sides by 6:
6(10x)/6 = 240(6) the 6's on the left cancel each other out so:
10x = 1440
so to find x we can then divide both sides by 10:
10x/10 = 1440/10
x = 144
So the length of the bottom section is 144 ft
The length of the top is 1/6 x = 1/6 x 144
= 24
The length of the middle piece is half 144 = 144/2
=72
So to check let us add them together:
72 + 24 + 144 = 240 !!!

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