a 120 foot long rope is cut into 3 pieces. the first piece of rope is twice as long as long as the second piece of rope. the third piece of rope id 3 times as long as the second piece of rope. what is the length of the longest piece of rope
Second x
First 2x
Third 3x
2x + 3x + x = 120
6x = 120
x = 20
third 60
Second 20
First 40
Let's assume the length of the second piece of rope is x feet.
According to the given information, the first piece of rope is twice as long as the second piece, so its length is 2x feet.
Similarly, the third piece of rope is three times as long as the second piece, so its length is 3x feet.
To find the sum of all three pieces, we can add the lengths of the individual pieces:
x + 2x + 3x = 6x
Since we know that the total length of the rope is 120 feet, we can set up the equation:
6x = 120
To find the value of x, we can divide both sides of the equation by 6:
x = 120 / 6
x = 20
Therefore, the second piece of rope is 20 feet long.
To find the length of the longest piece of rope (which is the third rope), we substitute the value of x into the expression:
3x = 3 * 20 = 60
Thus, the length of the longest piece of rope is 60 feet.
To solve this problem, we need to assign variables to the lengths of the three pieces of rope.
Let's call the length of the second piece of rope "x".
According to the problem, the first piece of rope is twice as long as the second piece, so its length is 2x.
The third piece of rope is three times as long as the second piece, so its length is 3x.
Now, we know that the total length of the three pieces of rope is 120 feet. So, we can form an equation:
x + 2x + 3x = 120
Combining like terms:
6x = 120
To solve for x, we isolate it by dividing both sides by 6:
x = 120 / 6
x = 20
Thus, the length of the second piece of rope is 20 feet.
Now, let's find the length of the first and third pieces of rope:
First piece: 2x = 2 * 20 = 40 feet
Third piece: 3x = 3 * 20 = 60 feet
Therefore, the length of the longest piece of rope is 60 feet.