SOLUTION: 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 3 times as long as the 2nd piece of rope. What is

Question 887874: 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 3 times as long as the 2nd piece of rope. What is the length of the longest piece of rope.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let the pieces be a,b,c. then we have
(1) a + b + c = 120 and
(2) a = 2b
(3) c = 3b
Put (2) and (3) into (1) and get
(4) 2b + b + 3b = 120 or
(5) 6b = 120 or
(6) b = 20
Then from (2) and (3) we get
(7) a = 40 and
(8) c = 60
Let's check this with (1).
Is (40 + 20 + 60 = 120)?
Is (120 = 120)? Yes
Answer; The length of the longest piece of rope is 60ft.
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