Whoa, take a breath Smores. The car finished its lap nearly 15 years ago and has long ago been sold for scrap.
mmm
You’re good so far.
No. Two laps are two miles. Two miles in four minutes is 30 mph.
No. Thirty plus sixty is ninety. Ninety divided by two is forty-five.
I’m not sure what you’re trying to say here but the numbers aren’t going to work.
Zombie thread or not, the original problem exposed an interesting cognitive quirk for me. My initial impression of the answer was “it has to be more than 90mph” but I wasn’t immediately sure how much, and I immediately dismissed trying to to the math in my head because the problem was presented in miles. If you took the same numbers but in kilometres (not converted to km, but 30km/h around a 1km track, etc) I would have come to the answer basically immediately. But as soon as I saw “miles” my brain just shut down and said “Nope, I don’t know how those work.”
The answer is the speed of light.
A lap is one mile. He drove 30 mph for one lap so he took two minutes.
two laps at 60 mph is also two minutes.
Do the math.
The sun has gone down and the moon has come up
And long ago somebody left with the cup
But he’s driving and striving and hugging the turns
And thinking of someone for whom he still burns
So, back in 2002, they were debating whether this was a trick question. I’d say it’s a tricky question, but it’s not a trick question.
At least IMHO, a trick question is a question constructed in a way to throw you off the track. This one isn’t constructed that way; the words we have for these things are constructed that way.
You’re looking at what look like whole numbers, but it’s really about fractions - not because of any deliberate setup, but because 30 mph and 60 mph are really fractions, they just don’t look like it. And people don’t think of them as fractions. (Not to mention, most people would rather not have to deal with fractions any more than necessary.)
And to answer the long-ago OP’s question, that’s why people are thrown by this problem. They don’t think of 30 mph as 30 miles/60 minutes. Even though it’s implicitly there in ‘mph,’ they don’t see it. You need to think about this problem in the right way to solve it (or rather, realize there’s no solution), and the right way to think about it is encoded in those three little letters, mph. But most people will just think, 30 and what average to 60? Well, 90, *duuuuh. * :smack:
When the sun goes down, and the moon comes up
I turn into a teenage goo goo muck
As bad as I am at any math beyond the basic stuff, logic puzzles like this rarely stump me. That’s why I reject the " higher math is necessary to learn to think logically" trope.
No doubt, higher math will help you think logically, if you’ve got an aptitude in that direction. (Not so much the material, but rather the fact that most of the problem sets in graduate-level math consist of doing proofs. You either learn to think logically, or you flunk.) But it’s certainly not the only route there, by a long shot.
And the math in math-related brain teasers is usually just grade-school arithmetic, with occasional forays into first-year algebra from junior high. So it’s not like you need heavy-duty math for the brain teasers. If I ever see one that requires calculus, it’ll be the first time for me.
Exactly correct. As a noted math educator once pointed out, “Trick questions are not okay. Tricky questions, on the other hand, are encouraged.” This is absolutely the second, not the first, for all the reasons you give.
I’m intrigued, looking back over the thread at someone’s comment that this question is “really” about semantics and not about math at all. Quite the contrary: it’s a math question. It’s a good bet that people who answer 90 mph don’t really understand how time/distance ratios work. If I taught the appropriate grade level, I don’t know if I would use the question as part of an assessment; but it could be very useful for probing kids’ actual understanding.
He’s going the distance
He’s going for speed
She’s all alone (all alone)
In her time of need
I would agree. The same knowledge required to solve this question is required to solve a similar question with a more mundane (but still somewhat tricky) answer. Instead of how fast to average 60 mph over the trip, how fast would you have to go to average 45 mph? It requires knowing average speed = distance/time. We know it’s a 2 mile trip. So to average 45 mph over the course of two one-mile laps, we would need to traverse 2 miles in 2/45 of an hour, or 2 2/3 minutes. Since the first mile was at 30 mph, that took 2 minutes, meaning we need to cover 1 mile in 2/3 minutes for the second lap. That works out to 90 mph.
If we followed the same principles (as has already been stated in this thread years ago), we would realize that an average speed of 60 mph means traversing 2 miles in 2 minutes. At 30 mph, our first mile will have taken 2 minutes, meaning the second mile must be instantaneous (or simply not possible.)
It’s the same math to get the answer to the modified question as it is the OP’s question. I don’t really find that to be a trick question so much as a question that anyone who understands the principles involved to be able to get. And the benefit of asking the question in this way is that you don’t actually need to do much math to figure it out (it’s something you can easily figure in your head), whereas in my question, you actually do have to a little bit of work.
I thought I already killed this thread once. The sad thing is that when I was reading this and came to the post about how to answer the question if the average was 40 mph I immediately wanted to correct the poster but reading on I saw that somebody already had. I was going to just quote their post but I thought it might be piling on. Today I came back to the thread and managed to notice that not only was the thread 15 years old, but the poster who insisted on correcting the post that I was going to quote was myself. Apparently, I am still insufferable.
Funny enough, that is literally correct (that is, in following the order of operations 30+60/2 does equal 60), but the expression you want is (30+60)/2, which, as noted before, is 45. It almost looks to me as if you typed 30+60/2 into Google or a calculator app or something and accepted the answer that came out.
Just do a little sanity check: if you want the average of the numbers 30 and 60, it’s going to be a number right in between both of them. 60 is not a number that looks to be midway between 30 and 60, does it? Even if you can’t do this in your head, you should be able to tell that numbers like 15, 60, 90 simply cannot be the average because the answer must be between 30 and 60.
Similarly, how can two laps at 30 mph average to 45 mph? Think about it. Does that make sense to you? If I’m going 30 mph the whole time, I’m going 30 mph, no matter how far I go. The distance is immaterial to my average speed.
These little sanity checks should tip you off that something is wrong with the way you’re approaching the question or setting up your equations/expressions. Don’t just plug in numbers in a formula or calculator and accept whatever answer you get before thinking about whether the answer makes sense. I’ve been saved many times on math and science tests involving math by sanity checking my answers and realizing I’ve missed a decimal point somewhere, or I forgot to convert units, or I didn’t take a reciprocal somewhere, etc. See if the answer makes sense in terms of the problem.
I’m just glad that Mary didn’t go to the store and buy 300 melons…no one ever goes to the store and buys 300 melons! 
Here is a related question. Which would do more for reducing CO2: raising your gas mileage from 20 to 40 MPG or raising it from 40 to 100 MPG?
Raising it from 20 to 40 exactly halves your fuel consumption and CO2 generation. You can’t do better than that, no matter how high you raise it unless you stop burning fuel. Going from 40 to 100 reduces it to a fifth of your original consumption but since 1/2 - 1/5 = 3/10, you have carried out a reduction only 30% of your original consumption by this.
I disagree that it is not a trick question. A non-trick question supposes that there is a valid answer to the question. There is no answer to the question “how fast do you need to go to…”.
Why I said speed of light because of the impossibility. 
Maybe. But that has nothing to do with what people get wrong about the question. It could be this instead:
You drive one lap at 30 mph. How fast do you have to drive a second lap in order to average 45 mph?
Most people will answer 60 mph. The actual answer is 90 mph. The flaw in people’s thinking isn’t that they thought there was an answer but it didn’t exist; it was that you can’t average rates with the arithmetic mean.
For a lot of folks there’s probably a tendency to make these problems harder than they should be. I agree that the math is pretty low level; maybe it’s advantage when it comes to solving these brain teasers to not know too much.
You can’t do a distance weighted average, you have to do a time weighted average. You’ve driven two minutes at 30 mph, you need to drive two minutes at 90 mph to average 60 mph. You need to drive three miles at 90 mph, and the constraint of only driving one lap is what makes it impossible.