Practical Pat was asked to cut a 99 foot rope into three smaller, equal length ropes.

However, as usual, Pat couldn't find the measuring tape, so a guess took place!

When the tape was finally found (it was under a hat), Pat discovered that:

the second piece of rope was twice as long as the first piece, minus 35 feet

the third piece of rope was half the length of the first, plus 15 feet

How long were each of the pieces of rope?

Puzzle Copyright © Kevin Stone

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Hint

Only one of the ropes was exactly 33 feet.

Answer

First = 34 feet.

Second = 33 feet.

Third = 32 feet.

Reasoning

This question can be solved using algebra. If we call the length of the first rope A, we have:

Rope 1 = A

Rope 2 = 2 x A - 35

Rope 3 = 0.5 x A + 15

The three ropes add to 99 feet:

99 = Rope 1 + Rope 2 + Rope 3

99 = A + (2 x A - 35) + (0.5 x A + 15)

99 = 3.5 x A - 20

119 = 3.5 x A

34 = A

Giving:

Rope 1 = 34 feet

Rope 2 = 2 x 34 - 35 = 68 - 35 = 33 feet

Rope 3 = 1 ÷ 2 x A + 15 = 1 ÷ 2 x 34 + 15 = 17 + 15 = 32 feet

Double-Checking

Rope 1 + Rope 2 + Rope 3 = 34 + 33 + 32 = 99