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Let t1 be the time taken to drive the first half of the route.
Let t2 be the time taken to drive the second half.
Let d1 be the distance traveled in the first half.
Let d2 be the distance traveled in the second half.
Let x be what we want to know (namely, the average speed during the second half of the route).
Then the following relations hold:
40 * (t1 + t2) = d1 * d2.
20 * t1 = d1.
x * t2 = d2.
d1 = d2.
Use algebra to solve for x.
To average 40 mph requires completing the trip in a certain amount of time, and even without doing any algebra, I notice that you will have used all of the available time just completing the first half of the trip, so you're speed would have to be infinitely fast during the second half.
I am pretty confident in that conclusion, but a little algebra will increase my confidence, so let us calculate as follows: the time you have to do the trip = t1 + t2 = d1 / 40 + d2 / 40, which (since d1 = d2) equals d1 / 20, but (by equation 2) d1 / 20 equals t1, so t2 must be zero.
I expect a high probability of this explanation being completely useless to someone who professes being bad at math. Their eyes are likely to glaze over before the half way point and the second half isn't infinitely accessible either.
I already had the problem explained to me before I saw the grandparent, but I think you're right - I might have been able to puzzle it out, but it'd have been work.
Well, in the department of actual running, I have some kind of mysterious lung issue that means I need to gasp for air a lot even when I'm sitting still and have been for hours and it only gets worse if I try to do exercise more strenuous than a leisurely walk. (Armchair diagnoses appreciated, incidentally - so far I've stumped multiple doctors and new Google keywords are good.)
Here is something like the thought process that goes through my head when I encounter a problem of this approximate type:
I know what all those words mean. I could come up with a toy scenario and see what's interesting about this problem, that someone bothered to bring it up.
It might be the sort of question where coming up with one toy scenario doesn't answer it because for some reason it doesn't generalize. Like it could have to do with the distance. I don't want to come up with five different distances and work it out for all of them. I'd probably make an arithmetic mistake anyway. I can barely compose a mathematically accurate D&D character, and I'm way more motivated there than here. I'm not interested enough in this to do it in a calculator and then re-read the ticker tape. My eyes are swimming just thinking about it.
And because I'm not good at this, I would be reasonably likely to get it wrong, and then, no matter how much time I'd put into it myself, I would need to ask someone. I could get help if I asked. I am cute and friendly and there are helpful people around. I could get help even if I didn't work on it myself. That would be faster, and then I'd know the answer, and I have to ask anyway, so why not just ask? Why not save the work, and not risk wasting a lot of time on getting a wrong answer and having to stare at all those numbers?
Record yourself (audio and video) during one of your attacks and I'll have a much better idea. Right now, it's extremely hard to tell from your description. Obviously, actually listening to you with a stethoscope and being able to perform a few tests would help me even more, of course.
By "attack" do you mean "one of the hundreds of occasions throughout an average day where I attempt to take an especially deep breath to satisfy my customary air hunger" or do you mean "run around until you collapse, gasping, and record that"?
The latter. But wait, you only have attacks when you run?
Running, biking, walking too fast up a hill, jumping on a trampoline, playing DDR.
Ok, but those are all exercise. Do you ever get attacks from cold, from allergens, from waking up in the middle of the night, from fear, from pain, from eating too much before bedtime?
I've found in the past that I remember the right answer better if I can guess it first and then get confirmation. It doesn't help when I guess wrong, but when I guess right it's a win.
Has the lung issue been a problem for your whole life? Is it better at some times and worse at others?
I don't have a theory, but this seems like a reasonable starting point.
The lung thing has gone on for several years; I have a memory that doesn't make sense without it that has to have taken place in fall 2006. I don't remember exactly when it started but I have not always had it. (I suspect it began sometime after I started taking iron to treat my anemia, since no one ever connected the two; that would've been some months after I turned 17, so, late 2005-early 2006).
It does vary day to day and hour to hour, plus with what I'm doing (walking excessively briskly, or jumping around, or otherwise being active, makes it act up - it was outright crippling on one occasion last summer when I tried to bike a few blocks; I had to pull over and sit on the sidewalk for a while and then verrrrry carefully bike back, walking the thing up hills and only riding on levels and downhill.) There is an overall trend of worsening from year to year.
Asthma/reactive airway disease seems like the obvious thing here, so has that been ruled out? Did they have you blow into a thing to measure whether you were breathing a normal volume of air (spirometry)?
I have never had to blow into a thing. Since I have consulted plural doctors about this, I'm not sure why none of them would have thought of athsma if that were consistent with my symptoms. Why might that be?
Asthma usually shows up in childhood, not at 17, and maybe some of the doctors you saw assumed that previous doctors would have checked out the possibility of asthma already. The definitive test for asthma is called a methacholine challenge; basically you inhale a chemical that irritates your lungs, and if you're asthma-prone then you have trouble breathing (there is no physical activity involved).
It probably isn't a heart issue if you haven't always had it...those are usually congenital...but I could be wrong. (Also not a doctor). But it sounds very debilitating, and worth fixing.
That is troubling. Even if it isn't asthma it is definitely something to do with the lungs that influences breathing. Measurement of breathing capabilities should be one of the first things they do!
Honestly? No idea. Nursing student here, in no way a doctor. But if I were you I'd go to a doctor and describe my symptoms and say "Could I have asthma?" I'm thinking most likely outcome is they give you some meds to try, which could be a good thing, you know? Certainly before you go after any of the zebras you'll get by Googling around.
My other thought is it could even be a heart issue, if your lungs check out. I'm kind of..surprised...that no one is more concerned about an apparently healthy young person being unable to breathe, so I'm guessing your oxygen saturation isn't dropping to scary levels or anything.
Was this an intentional pun, an unintentional pun, or a misspelling of "pleural"?
What hypotheses did the doctors check?
Is it ok if I post this thread to my livejournal? A fair number of my readers are smart people with health problems, and they may either have heard of something like what you've got or may have information about the reliability of common tests for possible causes.
I don't know what the hypotheses were. I've had a chest x-ray, which I was told revealed nothing interesting.
Post away.
The link.
I've gotten a few replies so far. It's likely that all the replies will arrive within three days.
Who is 'no one' and which two did they fail to connect? Why do you say 'since'?
I'm not a doctor. But it sure sounds to me that your blood is just not carrying enough oxygen to support vigorous exercise. Which is by definition 'anemia'. Which comes in various forms, the most common of which can be treated by iron supplements, but the most serious of which have other causes and treatments. Just from what I read on the web, my guess would be you have 'pernicious anemia'.
I would strongly advise going to a doctor again, and asking for blood tests. Be sure the doctor is informed about any ways in which your diet is unusual. Good luck.
"No one" is a couple of internists, my dad and my uncle (both doctors), and various random people I mentioned it to. What I mean is that people who know I used to be anemic and that I now have this dyspnea problem have never asked "I wonder if you still have [anemia-related subcondition] and that's causing the dyspnea?"
The iron pills working was confirmed with a blood test. Before I took iron pills, my readings on some relevant feature of my blood were so low that I ought to have been fainting on a regular basis; after they were in normal range and I've been allowed to give blood several times since.
Sorry for deleting my comment. I've been doing this a lot lately - I write something and then notice that it's stupid for one reason or another. (In this case it was the armchair diagnosing/other-optimizing.) Didn't think you'd react so fast.
It's okay. (I hope my thought process is interesting anyway.)
Well your last paragraph was interesting in a way. In fact I don't understand it. The point of a puzzle is to stretch and work out your brain, not arrive at an answer asap. If you have a bus full of hostages whose fate depends on an arithmetical problem, it's indeed wiser to ask someone else. But such situations don't occur often. In fact I sometimes explicitly ask other people to avoid giving me any hints because I want to solve the puzzle myself. Asking for help is analogous to taking the bus instead of your morning run :-)
But well, I guess if you don't enjoy puzzles already, then saying things like "c'mon jump in, the water's fine" isn't going to influence you much. Some things you really have to try before you can see the fun contained within. I think most things I enjoy in life fall in this category...
I hate being frustrated. It happens to me very easily. I hate not knowing the endings to stories, I hate not knowing what I'm getting for my birthday, and the only way I can not hate not knowing the answers to math problems is by not giving a flying fuck about them at all - which isn't conducive to expending effort on solving them. I've generalized the "stop giving a fuck" self-defense strategy to other hatreds-of-not-knowing stuff, mostly to discourage people from teasing me with this neurosis. I believe that other people can enjoy various forms of not-knowing-stuff, or fail to hate it enough to override some competing desire to achieve knowledge on their own. But I don't.
So basically, I looked at that math problem, sort of cared about knowing the answer, and asked. I got an answer (actually, several) which were quick enough to suit me. If the only way I could have learned the answer were to work it out for myself - or sit through ten minutes of algebra lessons or something - then I would have defensively ceased to care, instead.
Once I know the answer - in this case, that after having gone halfway at 20mph, you need to teleport to get to point B in time - then I can tolerate some further discussion of the scenario or the underlying math (although not arbitrary amounts). This is much the same as how, when I know that character X and character Y in some story eventually get together (or find the MacGuffin, or die, or whatever major plot item), I can often put up with extended periods of wondering exactly when and how.
Mayo clinic, from my very limit experience, can be quite thorough. You will at least have many eyes on the problem and the more the better.
They can offer finical asstance as well if they are not in network for your insurance. http://www.mayohealthsystem.org/mhs/live/locations/LM/pdf/FinancialAssistanceBrochure.pdf
This isn't a very good example. Making D&D characters that fit the rules can be surprisingly tricky. There' s just a lot of data to keep track of and lots of little corner case rules.
theonlysheet.com
A mostly solved problem. Although this doesn't quite handle all possible combinations of those add on books. Like the one which can be gamed to create what amounts to adamantium nano-bots (which are actually fairly reasonable if you think about what a rational individual would do given the physics but are nevertheless not quite intended).
Manual arithmetic and rules knowledge would also be required to work out exactly how much damage can be done when using a locate spell to utterly obliterate nearly everything on an entire continent.
I have to agree that a shorter explanation with just words in it would be bettter for someone with significant aversive math conditioning.
It also doesn't help the explanation when you make an error. That should be d1 + d2.
Acknowledged.