# How deep is the water?

PBE6
Posers and Puzzles 16 Jul '08 16:47
1. PBE6
Bananarama
16 Jul '08 16:47
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?
2. uzless
The So Fist
16 Jul '08 18:041 edit
Originally posted by PBE6
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 ...[text shortened]... that the freshly cut stem now just barely crests the top of the water.

How deep is the pond?
4 feet
3. PBE6
Bananarama
16 Jul '08 18:15
Originally posted by uzless
4 feet
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.
4. forkedknight
Defend the Universe
16 Jul '08 18:25
Originally posted by PBE6
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.
It's a 5-12-13 triangle, so 12 ft.
5. forkedknight
Defend the Universe
16 Jul '08 18:27
but I've never seen a pond with flowers growing in it that has banks that steep ðŸ™‚
6. 16 Jul '08 19:03
The flower itself has no height? Just the stem.
7. eldragonfly
leperchaun messiah
16 Jul '08 23:56
Originally posted by PBE6
A woman walks by a pond...
How deep is the pond?
Insufficient information.
8. AThousandYoung
All My Soldiers...
17 Jul '08 02:50
Originally posted by forkedknight
It's a 5-12-13 triangle, so 12 ft.
That's one possibility, but are there any others?

It's clear that it's a 5-D-(D+1) right triangle, but is 5-12-13 the only one of those?
9. eldragonfly
leperchaun messiah
17 Jul '08 02:53
Wrong, unless this is another trick question. One is only given that a flower with a 1 foot stem is growing out of the water, and is removed.
10. AThousandYoung
All My Soldiers...
17 Jul '08 03:00
Originally posted by eldragonfly
Wrong, unless this is another trick question. One is only given that a flower with a 1 foot stem is growing out of the water, and is removed.
No, the stem reaches to the bottom of the pond. Only one foot extends above the water.
11. forkedknight
Defend the Universe
17 Jul '08 03:071 edit
Originally posted by AThousandYoung
That's one possibility, but are there any others?

It's clear that it's a 5-D-(D+1) right triangle, but is 5-12-13 the only one of those?
5^2 + D^2 = (D+1)^2
25 + D^2 = D^2 + 2D + 1
2D = 24
D = 12

It's the only right triangle where the short side is 5 and the other sides have a difference of 1
12. eldragonfly
leperchaun messiah
17 Jul '08 03:07
Originally posted by AThousandYoung
No, the stem reaches to the bottom of the pond. Only one foot extends above the water.
insufficient information.
13. forkedknight
Defend the Universe
17 Jul '08 03:08
Originally posted by eldragonfly
insufficient information.
quit babbling and do some math.
14. AThousandYoung
All My Soldiers...
17 Jul '08 04:07
Originally posted by forkedknight
5^2 + D^2 = (D+1)^2
25 + D^2 = D^2 + 2D + 1
2D = 24
D = 12

It's the only right triangle where the short side is 5 and the other sides have a difference of 1
Ok. I suppose I should have realized to use the Pythagorean. I mean, I was a TA in middle school math all last year.
15. PBE6
Bananarama
17 Jul '08 16:59
Originally posted by eldragonfly
Insufficient information.
Now THAT would have been funny, but you wrecked it by being serious. ðŸ™„