Can Sheep Really Achieve a 10-Minute Flight Time?

[mattmns]

This problem has me baffled, I decided to put it in the brain teasers because it does not seem to be straight forward

Here is the problem. http://www.whitehouse.gov/kids/math/open/chl_82.html

 

[ceptimus]

You measure from the time the first sheep jumps till the last one does. So there are only 9 'jump intervals' in the ten minute period. Therefore a 'jump interval is 1.111... minutes. There are 54 such intervals in an hour, so the answer they're looking for is 55 (I guess).

 

[Bartholomew]

Well, the site does say your answer 55 is right, ceptimus. Of course, that assumes that the first sheep jumps immediately, and why would you assume that? If it takes 10 minutes for 10 sheep to jump the fence then each sheep clearly must spend the majority of his jumping time just eating grass or whatever. Why should the first sheep be any different? Unless maybe the starter's gun startles the first sheep into jumping...

 

[Bartholomew]

Or it could be a low-gravity situation so that each sheep actually DOES take a full minute just jumping...

 

[Gokul43201]

Ouch, I forgot to add 1 at the end

I tried 54, but that was wrong. Then I tried 60, and then I quit.

 

[Math Is Hard]

I tried to work this problem out several times, but kept falling asleep. :zzz:

 

[spacetime]

Ceptimus, are you a scientist?

 

[dextercioby]

My first answer was 2145,2(8).They said it was wrong.Then i tried "George W.Bush is a d***head".They said "wrong" again.No that tey learned my IP number,i wonder how much time will pass till one FBI dude will show up at my door asking for explanation.

Daniel.

PS.I wonder if Mr.IQ<100 "Man of the Year 2004" could figure out the answer without puttin' those sheep jump...

 

[tribdog]

I had a buddy who lived on a ranch. I spent a weekend on the ranch when I was little. He said watch how stupid these sheep are. He got a bunch of sheep running around the perimeter of a pen. Then he took a broom stick and held it in front of the sheep. the first sheep jumped over the stick, the second jumped over the stick. Then he took the stick away. The third sheep jumped over the spot where the stick used to be, the fourth sheep jumped over the non-existent stick, the fifth jumped etc.

 

[DaveC426913]

"...kept falling asleep..."

OK, now that's funny.



"...watch how stupid these sheep are..."

Actually, you could think of that as quite a brilliant trick.

Why wait to see danger yourself? Especially when, in a dense pack, you'll never see it in time. Anticipate.

There are advantages to living in a pack.

 

[DaveC426913]

"...assumes that the first sheep jumps immediately, and why would you assume that?"

1] Because it is counterproductive to begin measuring the duration of an event from any time other than when the event begins.

2] Because you set the sheep in motion, *then* hit the stopwatch when the first one leaps, not the other way around.

 

[Bartholomew]

1] Because it is counterproductive to begin measuring the duration of an event from any time other than when the event begins.

2] Because you set the sheep in motion, *then* hit the stopwatch when the first one leaps, not the other way around.

In a practical sense, if you have 10 sheep and you need to get them to leap a fence (let's say you get paid for every sheep that leaps the fence) you'd be timing from when you start TRYING to get them to leap the fence. So you start trying... and then a little while later the first sheep leaps the fence.

It's like, if an assembly line can produce X products an hour, you don't get to "pick the hour" to fit an extra product into the hour. Or in a human hurdling event, you don't time it from the point when the hurdler clears hurdle #1; you time it from when he starts running.

 

[matthyaouw]

I had a buddy who lived on a ranch. I spent a weekend on the ranch when I was little. He said watch how stupid these sheep are. He got a bunch of sheep running around the perimeter of a pen. Then he took a broom stick and held it in front of the sheep. the first sheep jumped over the stick, the second jumped over the stick. Then he took the stick away. The third sheep jumped over the spot where the stick used to be, the fourth sheep jumped over the non-existent stick, the fifth jumped etc.

It could be quite a useful trick if they were wild animals moving in a closely packed herd. If you can't see any obstacles because of the animal in front of you, the best bet is to follow in the exact footsteps of the animals in front that can see what's coming.

 

[BobG]

It could be quite a useful trick if they were wild animals moving in a closely packed herd. If you can't see any obstacles because of the animal in front of you, the best bet is to follow in the exact footsteps of the animals in front that can see what's coming.

I agree. In high school, I used to run cross country. There were quite a few races on golf courses. Having the instincts of a sheep would have come in quite handy when the two guys in front of me split apart to reveal one of those ball washers.

It didn't even work that good.

 

[ceptimus]

In a practical sense, if you have 10 sheep and you need to get them to leap a fence (let's say you get paid for every sheep that leaps the fence) you'd be timing from when you start TRYING to get them to leap the fence. So you start trying... and then a little while later the first sheep leaps the fence.

It's like, if an assembly line can produce X products an hour, you don't get to "pick the hour" to fit an extra product into the hour. Or in a human hurdling event, you don't time it from the point when the hurdler clears hurdle #1; you time it from when he starts running.

I agree. The whole puzzle is badly designed and worded in my opinion - why would only one sheep per minute (roughly) jump the fence, and why would it be a regular thing anyhow? I'm sure we could all think of better ways of framing the same puzzle - maybe a dripping faucet, or changing traffic signals - the number of advert breaks on TV - all would be better than these sheep.

That's why I said, "...the answer they're looking for..." I don't agree that it is the correct answer.

 

[mattmns]

So they were looking for 55 Also, I agree with you, that was an akwardly worded problem

 

[RandallB]

Because you set the sheep in motion, *then* hit the stopwatch when the first one leaps, not the other way around.

Good answer Dave and obvously the point of the problem.

Another form of the same problem:
How long does it take 10 sheep to jump a fence at a rate of one sheep per minute?

Lets see – should be start timing when they start walking across the field toward the fence -- or when the first one jumps.

Also along the line of:
When will the 200th decade end?? 2009 or 2010

 

[Bartholomew]

By your reasoning: I can run a mile in no time at all.

You set me in motion, *then* hit the stopwatch when the first mile is finished. Voila! One mile run in zero seconds.

Edit: The point is that if a sheep takes a minute to jump a fence, obviously more than the time the sheep spends actually airborne is important, just as more than the time I actually spend crossing the finish line is important. You count all of it.

 

[RandallB]

Bartholomew

your starting to convice me you might actually get this one wrong!

I'll change to help you fix the error you just made. If ten runners finish at 10 second intervals. How long will it take all 10 to cross the finish line.

 

[Bartholomew]

The point is that more is involved in jumping than the time actually spent airborne. "Crossing the finish line" is analogous to "landing on the ground on the other side of the fence." It is not analogous to "jumping the fence," which encompasses the entire process, in this case from dawdling to landing.

How long does it take a physicist to discover something major? Answer (by you): a few seconds for final insight. Correct answer: years.

 

[Bartholomew]

Analyze it semantically:

"If it takes ten sheep ten minutes to jump over a fence one at a time, how many sheep could jump over the fence in one hour?"

The key words are, "if it takes." How do you interpret that? One interpretation is that the total time spend actually jumping, actually airborne, is 10 minutes. This is the perfectly literal interpretation of the question--the jumps themselves occupy ten minutes of time--and as I mentioned would require a rather low-gravity environment. (Edit: Or a high cliff and sheep parachutes...)

Your interpretation is that the time occupied by the jumping is from when the first sheep actually leaps from the ground to when the last sheep lands on the ground. Here you only count the actual airborne time of the FIRST sheep, but you count ALL of the time when the OTHER sheep are just bumbling. Why do you do this? Who knows?

The most rational interpretation is that the time occupied by the jumping is start to finish, from when the first sheep starts on that meandering voyage to the fence to when the last sheep lands on the ground. ALL of that time can be said to be taken up by the jumping activity.

 

[NoTime]

One interpretation is that the total time spend actually jumping, actually airborne, is 10 minutes.

Well, if a cow can jump over the moon, then it seems reasonable that sheep might very well manage a 10 minute flight time.
That probably is the reason there is a little lost sheep problem.

Now where did that plate and spoon go...

:zzz: