30 ft pipe is broken in three pieces. The shortest piece is 6ft. shorter than the longest piece. The medium length piece is 2/3 the length of the longest
What is your question?
I need to solve for the longest section = L
Is this the equation I should use? How do I solve this?
30ft = L-6ft + L(2/3) + L
To solve this problem, let's assign variables to the lengths of the three pieces.
Let's call the length of the longest piece "x" (in feet).
According to the problem, the shortest piece is 6ft shorter than the longest piece, which means its length is (x - 6) ft.
And the medium length piece is 2/3 the length of the longest piece, so its length is (2/3)x ft.
Now, we know that when we add up the lengths of all three pieces, it should equal the length of the original 30 ft pipe. So we can create an equation:
(x) + (x - 6) + (2/3)x = 30
Now we can solve this equation to find the value of x, which will give us the lengths of all three pieces.
To solve the equation:
1. Distribute the (2/3) to the x:
x + x - 6 + (2/3)x = 30
2. Combine like terms:
(5/3)x - 6 = 30
3. Add 6 to both sides of the equation:
(5/3)x = 36
4. Multiply both sides by the reciprocal of (5/3), which is (3/5):
x = 36 * (3/5)
5. Simplify:
x = 18 * 3
x = 54
So the longest piece is 54 ft, the shortest piece is (54 - 6) = 48 ft, and the medium length piece is (2/3) * 54 = 36 ft.
Therefore, the three pieces of the broken pipe are 54 ft, 48 ft, and 36 ft in length, respectively.