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# A rod that weighs 20 pounds is cut into two pieces so that one of the

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Math Expert
Joined: 02 Sep 2009
Posts: 51243
A rod that weighs 20 pounds is cut into two pieces so that one of the  [#permalink]

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25 Sep 2018, 04:12
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:29) correct 50% (01:23) wrong based on 36 sessions

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A rod that weighs 20 pounds is cut into two pieces so that one of the pieces weighs 16 pounds and is 36 feet long. If the weight of each piece is directly proportional to the square of its length, how many feet long is the other piece of rod?

(A) 9
(B) 12
(C) 18
(D) 24
(E) 27

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A rod that weighs 20 pounds is cut into two pieces so that one of the  [#permalink]

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25 Sep 2018, 04:33
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Bunuel wrote:
A rod that weighs 20 pounds is cut into two pieces so that one of the pieces weighs 16 pounds and is 36 feet long. If the weight of each piece is directly proportional to the square of its length, how many feet long is the other piece of rod?

(A) 9
(B) 12
(C) 18
(D) 24
(E) 27

$$Weight = k*(Length)^2$$
16 = k (36)^2
i.e. k = 16/1296

Remaining weight = 20-6 = 4

Now, $$4 = (16/1296)*L^2$$
i.e. $$L^2 = (4*1296)/16$$

i.e. $$L = (2*36)/4$$

i.e. $$L = 18$$

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A rod that weighs 20 pounds is cut into two pieces so that one of the &nbs [#permalink] 25 Sep 2018, 04:33
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