A 120-foot long rope is cut into 3 pieces. the first 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?
a 20 feet
b 40 feet
c 60 feet
d 80 feet
why and thankyou!!
let the second piece be x ft long
then the first piece is 2x ft
and the third piece is 3x
x + 2x + 3x = 120
take it from here ....
thanks
Longest C.60, and 1st 20, 2nd 40.
20+40+60=120
To solve this problem, let's first represent the length of the second piece of rope as x.
According to the problem, the first piece of rope is twice as long as the second piece, so its length would be 2x.
Similarly, the third piece of rope is three times as long as the second piece, so its length would be 3x.
Now, we know that the sum of the lengths of all three pieces is equal to 120 feet. So we can set up an equation:
x + 2x + 3x = 120
Combining like terms, we have:
6x = 120
To solve for x, we divide both sides of the equation by 6:
x = 120 / 6
x = 20
Therefore, the length of the second piece of rope is 20 feet.
To find the length of the longest piece of rope, we substitute the value of x back into the equation:
3x = 3 * 20
3x = 60
Hence, the length of the longest piece of rope is 60 feet.
Therefore, the correct answer is option c) 60 feet.