Originally posted by eldragonfly
Just answer the question, why should i assume that the lake is more than 1 foot deep, that's the flower + the one foot stem? Fact is this is another silly word problem, not very insightful. If you would be so kind PBE6 since i'm willing to let by-gones be by-gones, please pm me the solution. i just want to see the math, i promise i won't criticize the reasoning or lack thereof behind it.
No need for a pm, spanky, just refer to the following un-edited posts:
#1 "A woman walks by a pond, and sees a beautiful flower growing on a stem in the middle of the pond. She finds a 5 foot stick by the pond, which just allows her to reach the flower and drag to the edge, where the flower just touches the water. She then picks the flower with 1 foot of the stem attached, and lets the rest float back to the centre of the pond. She notes that the freshly cut stem now just barely crests the top of the water.
How deep is the pond?"
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#2 "Nope, but I should clarify the wording in the problem.
The distance from the edge of the pond to the flower is 5 feet, and the flower sticks out 1 foot above the surface of the water before being cut. You can assume that the flower stem is taught and remains a straight line from the flower to the centre-bottom of the pond at all times."
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Let the original length of the flower stem be R. The length from the edge of the pond to the flower is 5 feet, and 1 foot is plucked from the stem by the lady, leaving the stem R-1 feet long. This is the depth of the pond since the stem now only barely crests the water when returned to its original position. Since the flower just touched the water when dragged to the edge of the pond, we know that the length from the edge of the pond to the centre-bottom is R.
Now, we have a right angle triangle with R as the hypotenuse, 5 as one leg and R-1 as the other. By the Pythagorean theorem, we have:
R^2 = (R-1)^2 + 5^2
R^2 = R^2 - 2R + 1 + 25
2R = 26
R = 13
Since R-1 is the depth, the answer to the question is:
R-1 = 13 - 1 = 12.