I’d expect most of them to say, “This is the fifteenth time I’ve seen this stupid brain teaser. I may have gotten it wrong the first time I saw it, but I was in second grade then. $1.05 and 5¢, just like all the other times.”
I understand that, but was it supposed to be the problem i linked to? Otherwise it’s a problem what is the sum of a pineapple plus an alarm clock?
Yeah, if you asked this among my coworkers everyone would get it right without batting an eye, and they’d wonder how you got in the building.
I don’t know, we’ll have to wait for the other person to reply
Yeah, seen that one more than a few times too, though I think the first time may have been fourth or fifth grade rather than second. I still remember the feeling of the light bulb going on when I saw the answer. 
I have not heard of that in years. It took a long time after the first time before the light bulb came on. Even given the answer I couldn’t get past the idea that you could average 30mph if you just went fast enough. I think I had to just take the hill out of the problem and consider a flat line 2 miles long before I finally got it.
You’re average person, has below average intelligence.
What gets it for me is figuring out how many minutes it should take.
In other words, at 30 miles an hour average, it should take you 2 minutes to go a mile, or four minutes to go two miles. If you want to average 30 mph, you have to take 4 minutes to go the entire trip.
At 15 miles an hour, it takes you four minutes to go a mile.
You have 0 minutes left for the return trip if you want to average 30 mph.
Since you’ve already taken four minutes to go the first mile, you have to go at warp speed to take four minutes to go two miles.
But I have to reason through all of that every time I hear the puzzle in order to understand the answer.
Beam me to the bottom of the hill, Scotty! 
The book I saw this one in (I think it may have been that early 1960s Time-Life book on mathematics that I saw so many cool things in for the first time) did that sort of explanation, and I remember thinking, “oh I see now, that’s how I should have thought about it!” because of course I got it wrong before I read the answer and the explanation.
Wherever it was, I don’t think they bothered with the hill or the condition of the car. Just “you’re driving two miles, you go the first mile at 30 mph, how fast do you have to go the second mile to average 60 mph for the two miles?”
To me, this is the real skill involved in any of these questions, taking the information given and reframing it in different ways that help you to see the question in a new light.
Asking yourself the question in terms of “how long to cover that first mile?” can lead you to think “OK, so then how long would it take to cover the full distance at an av. 30mph?”
From that you quickly get to an “ah-ha!” moment.
The maths is trivial, the innovative approach sometimes has to be learned, like cryptic crossword clues.
Yeah, but he’s halfway to writing his master’s thesis in the philosophy of language. That, and a buck eighty-five will get you a cup of coffee at Starbucks.
Stranger
That’s a common rough approximation that most people get wrong. What you really have to do is set it up so that X represents the completed thesis…
No, I’m not.
The key is working on the first half of the remaining work…
Zeno of Elea came up with “the Dichotomy” paradox while working on his graduate thesis about the Paradox of Place. His failure to complete the thesis is why he was not invited to join the National Academy of Sciences. Meanwhile, John the Pencil Guy apparently didn’t realize that he could have purchased 21 pencils for instead of buying that ridiculously overpriced $1.05 pencil, and then sold the excess 20 at 100% markup to people who think cheap pencils cost ten cents. He scored too low on the SAT to beat Aunt Becky’s daughter into USC and ended up pushing a broom at Staples Center in obscurity.
I had a point when I began this but it has since vanished like the career opportunities of a philosophy major upon graduation.
Stranger
Would you like fries with that?
There’s no way to make that work. It relies on using two different interpretations for different parts of the problem. Either they’re statistical chickens or not. If they’re not, you have to at least ascribe some real meaning to the half chicken and egg. If they are, you can only round after the fact, not before determining rate.
I don’t get any of that. I suck at math, but it’s not that difficult really. We expect egg production to be described as the number of eggs 1 chicken lays in 1 day. But it’s just applying that rate to 1 1/2 chickens over 1 1/2 days.
1 1/2 chickens laying 1 1/2 eggs in 1 1/2 days is the same as 3 chickens laying 3 eggs in 1 1/2 days, and the same as 3 chickens laying 2 eggs in 1 day, or 1 chicken laying 2/3 eggs per day.
I had no idea how this worked when I first heard this math riddle as a kid, many years went by before I finally understood and worked through it, and I have to work through it every time I see it to explain it to myself, but it’s just describing a rate of egg production in an odd way.
This is the first time I encountered this problem. It is difficult but now I feel better knowing Einstein found it tricky too.
Wolfram Alpha says “no solutions exist”: 2/(1/15+1/x)=30 - Wolfram|Alpha
I had a really hard time understanding this even after I’d had it explained to me. I can’t really explain what’s wrong with the math except you’d end up dividing by 0 as the time in an MPH calculation.