Word problem on creating equation

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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?

Nov 1st, 2015

Thank you for the opportunity to help you with your question!

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


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 rope


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

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 1st, 2015

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