When I was in middle school, we had these awful geometry books where each chapter came to a conclusion with a difficult word problem. One chapter was called "The Grazing Goat" and the next was called "The Burning Candle." Bored and creative(?) creature that I was, I decided to waste class time by writing a word problem of my own: a morbid combination of the two called "The Burning Goat."
The Burning Goat
Farmer Bob has carelessly poured gasoline on his goat while refueling his tractor. Pleased with a job well done, Bob pulls out a cigarette and tosses the match over his shoulder onto the unsuspecting animal. Panicking, the flaming beast heads for a lake which is 5 miles due north of the barn. The barn is 12 miles due west of the goat. The goat runs at 25 miles per hour, but 2/3 of the way there, he falls into a ditch and breaks his leg, so his speed is reduced to 6 miles per hour. The goat can survive for one hour in flames. Will he make it to the lake before he is reduced to a smoldering stump?
((Written by nolan_ash, age 13(?) Well, I thought it was funny. >_>;; Bonus points to anyone who actually feels like solving this disaster.))
palmer_kun: The goat dies 0.41296 miles (2180 feet) from the lake.
[snipping out the math, go see context if you want it]
Also, that is one insanely fast goat, especially with a broken leg. Then again, if I was on fire, I'd run fast too.
Exploratory Question for bonus points: How many hit points must this goat have to survive for an entire hour on fire?
sparklemagpie: Presuming a standard 1d6 damage per round from the fire, and an averag 3.5 points of damage per roll... 10 rounds per minute, therefore, 600 rounds an hour...
2,100 HP to survive an hour on fire.
2,240 HP to survive the 640 rounds it would have taken the poor goat to actually get to the lake and not die.
.... damn that must be a high level goat. 0_o
palmer_kun: Given that animals get d8 hit dice, and assuming a goat has a Con of 10, that's an average of 4.5 HP per level.
A level 467 goat would have 2101.5 HP.
A level 498 goat would have 2241 HP
But you missed the 8 seconds extra, which is 2 more rounds. That's 2247 HP needed.
So we have a Level 500 goat, with 2250 HP, and it lives!
That goat also has a Base Attack of +375 o_O
sparklemagpie: And yet it failed a relfex save vs cigarette butt. 0_o
And all it's subsequent reflex saves.
Clearly this is like some super-old, uber experienced ANCIENT WYRM GOAT, with athritis, osteoperosis, and a neg 10 to his dexterity.
Poor washed up flaming supergoat...
It seems the context is now locked. For those who want it, I present the math here.
The goat dies 0.41296 miles (2180 feet) from the lake.
SHOWING MY WORK.
The square of the hypotenuse is equal to the sum of the square of the other two sides. 5^2 = 25 + 12^2 = 144 = 169 13^2 = 169.
The lake is 13 miles from the goat.
13 x 0.66666 = 8.6666 miles The goat travels 8.666 miles before breaking a leg. 8.6666 / 25 = 0.34666 It covers this distance in 0.34666 hours.
This leaves 0.65333 hours until death, and 4.333 miles to travel.
6 miles per hour x 0.65333 = 3.92 miles.
4.333 miles - 3.92 miles = 0.41296 miles remaining at the end of one hour.
The goat needs an additional 4.1296 minutes (4m08s) to reach the lake.
Context would have made math class MUCH more interesting.