Mr. Ho has a 120 foot rope. It is broken into 3 pieces. The second piece is twice as long as the first piece. The third piece is 3 times as long as the first piece. How long is the longest piece of rope?

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Let's call the first piece of rope is X foot.

2nd piece of rope is 2X foot.

3rd piece of rope is 3X foot

but we know that, total length of rope is 120 foot

X+2X+ 3X= 120

6X=120

X = 20 foot i.e first piece of rope

2X = 2*20 = 40 i.e 2nd piece of rope

3X = 3*20 = 60 i.e 3rd piece of ropeAnswer:

First Piece = 20 foot

2nd Piece = 40 foot

3rd Piece = 60 foot [Longest Piece of Rope]

we can also check that after adding all the pieces i.e 20+40+60 = 120 foot long. i.e original rope length

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