Compared to setting the poor goat on fire in the first place … not so wrong.
Incidentally, The Burning Goat would be a great name for a music festival, though not so much for a band.
And here I thought this would be about a pub. :dubious:
I’ll have to work that in if I ever run a game again. 
Maybe, out of his mind with pain and terror, he actually ran away from the lake?
MMMMMMMMMM… BBQ goat!
[SPOILER]That’s it. 
I see what I was doing wrong–I had him running towards the barn and then up to the lake, instead of calculating the hypotenuse of the triangle.
My modified calculation has him arriving roughly three minutes too late; unless we assume he’s equidistant with the barn to the lake, in which case he can get there in under half an hour, the goat rings up the curtain and joins the choir invisible, pushes up daisies, is an ex-goat, etc.
[/SPOILER]
One thing we’re forgetting to take into consideration: how long can a goat survive on fire?
We know he arrives to the lake 3-4 minutes after erupting into flames, but is this necessarily fatal, especially with todays ewesome technology? I’m not so sure.
Another good Metaquotes entry of the past few days is “meeting Tim Curry while he shops at your store”. Too funny. I giggled and cackled and squeed. 
[spoiler]That’s what I get - it’ll take him just over four minutes more than he has to get there, and I think the difference is just due to rounding.
My maths; he’s travelling the hypotenuse of a triangle with 5 and 12 mile long sides; that’s a 13 mile distance (using Pythagoras). He travels at 25mph for two-thirds of the way; that’s 8. 67 (rounding) miles. 25/8.67 = X, 60/X gives 20.7 minutes. Good time. Then things go downhill, as he now needs to cover 4.33 miles at 6 mph. 6/4.33 = Y, 60/Y gives 43.5 minutes. Altogether his trip will take 64.2 minutes.
Working back from that, he travels at 6mph for those last 4.2 minutes. I had to cheat here because I got completely confused, and made it easier by saying he was going at 1mph. 60/4.2 = Z, 1/Z = 0.07. He was actually going six times as fast, though, so that means he covers 0.07 * 6 = 0.42 miles. 1 mile is 5280 feet, and 1 foot is 12 inches, so 0.42 * 5280 = 2217.6, making him about 2217 feet, 6 inches away from the lake when he expires. [/spoiler]
Incidentally, both of these quotes have been combined into one icon.
You know, it just occurred to me that if someone had bothered to teach this goat to Stop, Drop and Roll, this whole tragedy may have been averted.
Or if someone had thought to tell the farmer that smoking could be bad for him, thus encouraging him to avoid the whole habit.
Inasmuch as Scuba_Ben was the first to calculate the answer, we tell him:
GOAT to the head of the class!
D & R
[spoiler]What you all (including the author of this problem) have overlooked is that the ditch into which the goat falls has 5.62 inches of muddy water in the bottom. The goat somersaults 1.34 times during its fall, then tips sideways, immersing 47.8 percent of its left side in the muck before scrambling out and resuming its run for life. The resulting dampening of the flames increases the goat’s runtime to?
No cheating, Kythereia; stop peeking at Revenant Threshold’s paper.[/spoiler]
Can we fire goat out of a PVC Cannon, thereby shortening his trip?
If only there were a thread about PVC Goat Cannons…
You could fire the goat out of a cannon, but while the trip is shortened, the increased oxygenation of free air on the burning goat coat would likely create a flaming goat comet appearance. Billy’s Comet!
Anyone up to writing a word problem entitled Burning Tim Curry while he shops with your goat?
The goat lives!
I get that it only takes the goat .41 hours to reach the lake. See, what you all neglected to realize is that the barn is at a latitude of 89.9277147 degrees north, so the total distance from the goat to the lake is actually only 5 miles, not the 13 everyone is assuming. Thank Pan for global warming, because without it, there wouldn’t have been that lake of melted snow for the poor goat to jump into.
Won’t anyone think of the kids?
Tris
Ooooh… very punny.