QUESTION: A 210 ft. long rope is cut into 3 pieces. The first piece of rope is 3 times as long as
the second piece of rope. The third piece of rope is 2 times as long as the second
piece of rope. What is the length of the longest piece of rope?
Let the three rope lengths be L1, L2, L3.
Then L1 + L2 + L3 = 210.
The first piece of rope is 3 times as long as the second piece of rope.
Therefore, L1 = 3*L2.
The third piece of rope is 2 times as long as the second piece of rope.
Therefore L3 = 2*L2.
Substituting for L1 and L2 into the 1st equation,
L1 + L2 + L3 = 3L2 + L2 + 2L2 = 210
6L2 = 210
L2 = 35
Therefore L3 = 2*L2 = 2*35 = 70
Longest piece of rope is L3 = 70 ft