Arocket 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 312 feet. find the length of the top section.

We want to find the length of the top section of the rocket given that we know the total length of the rocket and the relations between the length of each section. We will see that the length of the top section is 24ft.

So the information that we need to use here is:

Total length of the rocket = 312 ft

We can define:

We know that:

T = (1/8)*B

M = (1/2)*B

And:

T + B + M = 312ft

So we have a system of 3 equations:

T = (1/8)*B

M = (1/2)*B

T + B + M = 312ft

And we want to solve it for T, so the first thing we must do is isolate one of the variables in one of the equations, and replace that in the others.

We can see that M is already isolated in the second equation, so we replace it in the third to get:

T = (1/8)*B

T + B + (1/2)*B = 312ft

Now we have a system of 2 equations, now we can isolate B in the first one to get:

B = 8*T

Now we replace this in the third equation to get:

T + 8*T + (1/2)*8*T = 312ft

13*T = 312ft

T = 312ft/13 = 24ft

So the top section of the rocket measures 24 ft.

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The length of the top section is 24 feet.

Step-by-step explanation:

Let the bottom section of the rocket be x.

Let the middle section of the rocket be

Let the top section of the rocket be

Adding these three section will result in the total length of the rocket 312 feet.  

Thus, solving the equation results that .

Thus, the bottom section of the rocket is 192 ft.

To find the middle section and top section of the rocket, let us substitute the value of x in and  

Middle section =  

Top section =

the least common denominator is 40