Puzzle Details

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:

A) the second piece of rope was twice as long as the first piece, minus 35 feet (i.e. 2 x first, - 35).
B) the third piece of rope was half the length of the first, plus 15 feet (i.e. 0.5 x first, + 15)

How long were each of the pieces of rope?

First  = 34 feet.
Second = 33 feet.
Third  = 32 feet.

This question can be solved easily 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 = 1 ÷ 2 x A + 15

The three ropes add to 99 feet, so:

99 = Rope 1 + Rope 2 + Rope 3

99 = A + (2 x A - 35) + 1 ÷ 2 x A + 15

99 = 3.5 x A - 20

Adding 20 to both sides we have:

119 = 3.5 x A

So:

A = 119 ÷ 3.5

A = 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

Just to check:

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

As required.

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