A 120- foot long rope is cut into three pieces the first piece of rope is twice as long as the second piece of rope the third piece of rope is three tines as long as the second piece of rope what is the length of the longest piece of rope?

Please click on the Related Questions below.

To find the lengths of the three pieces of rope, we can start by assigning a variable to one of the unknown lengths. Let's say the length of the second piece of rope is x.

According to the problem, the first piece of rope is twice as long as the second piece of rope. So, the length of the first piece is 2x.

The third piece of rope is three times as long as the second piece of rope, so the length of the third piece is 3x.

We know that the sum of the lengths of the three pieces of rope is equal to 120 feet. Therefore, we can set up an equation:

x + 2x + 3x = 120

Combining like terms:

6x = 120

Now we can solve for x by dividing both sides of the equation by 6:

x = 20

Now we can find the lengths of the three pieces of rope:

First piece: 2x = 2*20 = 40 feet
Second piece: x = 20 feet
Third piece: 3x = 3*20 = 60 feet

The longest piece of rope is 60 feet.