A 120-foot-long rope is cut into 3 pieces. The
first piece of rope is twice as long as the second
piece of rope. The third piece of rope is three
times as long as the second piece of rope.
What is the length of the longest piece of rope?
Let the three pieces of the rope be x,y, and z respectively.
1) x=2y
2) z=3y
(Note: We deduce from these 2 equations that the longest part we want to find is z)
3) x+y+z=120
Substitute 1) and 2) in 3)
Hence we get: 2y+y+3y=120;
6y=120 ==> y=20 ft
Therefore, z=3y=60 ft
To find the length of the longest piece of rope, we need to determine the lengths of all three pieces.
Let's assume 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. So, the length of the first piece would be 2x.
Similarly, the third piece of rope is three times as long as the second piece. Therefore, the length of the third piece would be 3x.
Now, we know that the sum of the lengths of all three pieces is equal to the total length of the rope, which is 120 feet.
So, we can write the equation as x + 2x + 3x = 120.
Simplifying the equation, we get 6x = 120.
Dividing both sides by 6, we find that x = 20.
Therefore, the length of the second piece of rope is 20 feet.
Now, we can find the lengths of the other two pieces:
- The length of the first piece is twice the length of the second piece: 2 * 20 = 40 feet.
- The length of the third piece is three times the length of the second piece: 3 * 20 = 60 feet.
Finally, we can see that the longest piece of rope is the third piece, which has a length of 60 feet.