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?
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
Reasoning
Since 210 = 2 x 3 x 5 x 7, 12357 is the only way to get a 5-digit number, in ascending order.
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Puzzle 19
At the equator the radius of the earth is 6,378 km, so its circumference is almost exactly 40,000 km.
Imagine we had a long rope which went around the equator, this would of course be 40,000 km long.
If we now placed 1 metre sticks vertically all the way around and lay the rope on top of these sticks (so the rope would be 1m higher all the way around) how much extra rope would we require?
