Puzzles
Pole position
Two poles stand vertically on level ground. One is 10 feet tall, the other 15 feet tall. If a line is drawn from the top of each pole to the bottom of the other, the two lines intersect at a point 6 feet above the ground. What's the distance between the poles?
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The two poles can be any distance apart; the distance does not affect the heights.
Extension
If the heights of the two poles were 12m and 24m tall, what height would the intersection of the lines be?
If the heights of the two poles were \(a\)m and \(b\)m tall, what height would the intersection of the lines be?
Burning ropes
You have two ropes and some matches. Each rope, if lit at its end, will burn for 60 minutes. But the rate of burning is not regular, so cutting a rope in half doesn't result in a burn time of 30 minutes.
How can you use the ropes to time exactly 45 minutes?
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Light one rope at both ends and the other at one end. When the first rope finishes burning, light the other end of the second rope. The second rope will finish burning 45 minutes after the start.
Extension
What are all the possible times you can measure with two ropes? How about three ropes? Four ropes? n ropes?
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