Question 620351
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 !!!