second piece --- x
first piece --- 3x
third piece --- 2x
solve:
x + 3x + 2x = 210
the second piece of rope. The third piece of rope is 2 times as long as the second
piece of rope. What is the length of the longest piece of rope?
first piece --- 3x
third piece --- 2x
solve:
x + 3x + 2x = 210
2x_3x=210
According to the given information, the first piece of rope is 3 times as long as the second piece. So, the length of the first piece is 3x.
Similarly, the third piece of rope is 2 times as long as the second piece. So, the length of the third piece is 2x.
Now, we can create an equation to represent the total length of the rope:
Length of the first piece + Length of the second piece + Length of the third piece = Total length of the rope
3x + x + 2x = 210
Simplifying the equation, we get:
6x = 210
To solve for x, we divide both sides by 6:
x = 35
So, the second piece of rope is 35 ft long.
Now, we can find the lengths of the first and third pieces:
Length of the first piece = 3x = 3 * 35 = 105 ft
Length of the third piece = 2x = 2 * 35 = 70 ft
Therefore, the longest piece of rope is the first piece, which is 105 ft long.