A 210 ft. long rope is cut into 3 pieces. The first piece of rope is 3 times as long as

second piece --- x

first piece --- 3x
third piece --- 2x

solve:
x + 3x + 2x = 210

x+3x+2x=210

2x_3x=210

72

To find the length of the longest piece of rope, let's first define the variable representing the length of the second piece of rope. Let's call it x.

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.