…so what happened to the other dollar?
:::d&r:::
Well, it is a Brain Teaser. If they were clear and unambiguous, then they would just be ordinary questions. The point is to delude you into thinking you have the correct answer, when in fact, you don’t, because you didn’t read the question carefully enough.
What you have to catch is the 1 mile part. Why is that fact put into the question? Why is 1 mile important? What if it were five miles? If you only take in the 30 mph 1 lap and ? for lap 2 that will lead you to the wrong answer because you didn’t take in the 1 mile per lap.
The distance is unimportant. Clearly, I cannot average, after going distance X at Y, go distance X again so as to average 2Y, since I’d already be done.
Try changing the distance to 30 Miles – same answer.
RawDuke, I think you hurt your own question! The units you gave are impossible, but many people are stumped by the general puzzlers that involve calculating (seemingly) both time and distance simultaneously.
Try this, solvable puzzler. A lap is 50 miles, and Racer A goes 75 MPH full out. Racer B, conserving his Nitrous, goes 50 MPH for one lap. How fast does he have to go on the second lap to catch Racer A?
So this falls under the heading of “trick question,” which people hate. Step back from the keyboard and prepare to receive a Wet Willie you will not soon forget.
ACE, I need to assume that both racers finish the second lap at the same time? If not, racer b could catch racer by flooring it and going, say, a million MPH and catch A in, ummmm, real quick!
Otherwise, at 75 MPH, A will finish 2 laps in 1 1/3 hours. Racer B would finish one lap in one hour, that leaves him 1/3 hour to travel 50 miles, which he could do at 150 MPH. Correct?
ETHILRIST, I would be happy to step back and receive that “Wet Willie” and might even enjoy it!
Would you first:
a. Explain just what a Wet Willie is?
b. Explain (and I’m not trying to be rude here, I’m truly curious) why do you think this is a “trick?” What is it about this teaser that is ambigous? I guess I don’t see why people feel tricked.
Your answer is correct.
The original question is set up to “trick” one, IMO, not by the wording, but by the impossible answer, and the use of a track oval, instead of a straight line back and forth.
That said, I enjoy a good trick question, though “Infinite” feels a little unsatisfying.
-Ace
I read this at work, and it just didn’t sink in. I just re-read it. I didn’t get the “distance in unimportant” part. I guess the ability to visualize a one mile track helped me figure it out.
But you’re right, ACE the distance doesn’t matter. This is a very elegant explaination.
But I still have to disagree with the idea that this is a “trick” question.
To me, this is a “trick” question:
“Which weighs more, a pound of feathers or a pound of gold?”
To answer this question correctly, you need to know that gold is weighed in Troy measurement, in which there are 12 ounces to a pound. Which means that a pound of feathers weighs more.
Funny, when I read the thread title, I knew it was either going to be the question about the three men who pay $30 to stay at the hotel, or this one.
The thing to remember is than there are different sorts of averages. For most things the most common average is the mean (add them all up and divide by the number of things).
But average speed means “total distance travelled divided by total time taken” or “speed that if I had gone the whole way at, would have taken me the same time” because this is the only one that’s any use.
The trick is that this is different to the normal average. Both are averages, but the one wanted here is worked out differently, as many people have pointed out.
How about the speed of light? No time passes for you as you complete the second lap, so you manage to complete both laps in two minutes. In order to average faster than 60 mph, simply travel faster than the speed of light. 
So the smartass answer to this question is that the second lap is made in 0 seconds. There would be no way for an observer or the driver to discern whether or not the car had made the second lap.
The laws of physics don’t apply here according to how the question is worded. As dwc1970 pointed out, you’d have to have a car that could instantly accelerate to 30MPH and travel exactly one mile for the first lap (not to mention we’re not taking into account tire friction, air resistance, engine performance consistancy, and inprecise measurement equipment). Even if the required average were dropped to 40MPH for both laps, the second lap would need to be driven at 50MPH and the car would need to instantly accelerate from 30MPH to 50MPH exactly at the finish/start line. Even The Fast and the Furious didn’t have cars like that.
Actually, I don’t see any trick in the way the problem is worded. It really is a legitimate question–there’s no trick, just an answer that most don’t expect (or even accept, many times). In fact, try this wording:
You drive the first lap averaging (so any time “wasted” for acceleration or whatever is taken into account here) 30 mph. How fast must you average for the second lap in order for the average speed for the entire trip to be 60 mph?
I guarantee most people will still answer 90 mph, though the answer is still “impossible” (minus any relativistic effects ;)).
Is the 30 constant in the first lap?
The distance is important in that you have to think about the distance the driver has to travel. Yes the answer is the same no matter how big the track but if a person only thinks
1 lap = 30
both laps = 60
so 2nd lap must = 90
is not taking into account the lap = 1 mile in the original question.
Because you are not traveling at laps per hour, you doing miles per hour.
Actually, this isn’t smartass at all. It’s correct.
Even at the speed of light, some time would elapse (the time it takes light to travel one mile)
You’re talking a smidge under 60 MPH average, but it’s still under.
If you’re interested in why people have trouble with math problems like this one, may I recommend the wonderful book Mathsemantics by Edward MacNeal? It may be out of print, but if you can track down a copy, it’s well worth reading.
We actually ask this question in our interviews for graduates. A remarkable number give the wrong answer. Personally I gave the right answer within about 2 secs. And I hadn’t heard it before. It just seems obvious to me.
It’s obvious because when you average a speed, you should do so weighted by the time you travelled at that speed. For instance if you travel 2 hours at 30mph and 1 hour at 60mph then your average speed is (2x30 + 1x60)/(2+1) {Note this is just another way of saying speed = distance/time}
In the question you can’t average 30 + 90 to get 60 because you will have travelled one lap in 2 mins and one lap in 40 seconds. Anyone that has ever worked with weighted averages should immediately recognise that that doesn’t work. In this instance the average of 30 and 90 is (30x2 + 90x0.6666)/2.6666
pan
a. To perform a Wet Willie, one first wets one’s index finger to the first joint by inserting it into one’s mouth; then, one approaches the Willie recipient and inserts it into the (hopefully unsuspecting) victim’s ear and rotates the finger vigorously. This is rumored by some to be strangely pleasant, and by others to be monumentally unpleasant.
b. When presented with a word problem, the basic assumption is that there is a way to solve the problem. If, in fact, there is no answer, it’s kind of irritating. Suppose, for example, I presented you with a popup ad saying, “Punch the monkey to win $1,000;” if you punched the monkey but didn’t win the $1,000 because of some bizarre arbitrary reason, you would be justifiably annoyed.
Such questions are not about logical thinking or being good at physics or anything else. They are about stating a simple question in the most obscure way possible in order to make a fool out of the person you target with your little practical joke.
How many people would miss it if it were asked more clearly?
“If you travel a mile at a rate of 1/2 mile per minute taking two minutes how fast will you have to travel for a second mile to cover a total distance of 2 miles in two minutes?”
It is the intentionally poorly asked question not anyone’s answer to it that is in error.
Someone mentioned that they use this question for interviews for graduates. What?!?!
If I were met with a silly practical joke by someone I was interviewing with for any reason I would at least refuse to play and at most walk out. I cannot imagine why you would want to subject a person already in a stressful situation to a pointless amusement for you and you fellow interviewers. I honestly cannot imagine any useful information you could possible expect to garner by asking the question.
Playing a practical joke on someone by dropping rotten eggs on them is no worse than playing this kind of practical joke. There are about a dozen ways to write a joke question. Some have a “correct” answer. Some, like this, have no answer. When people hear one they immediately start thinking, “Which kind of joke is it?” not, “What is the right answer?” Even in this thread there was as much discussion about what kind of a trick question it was as there was discussion about what the “right” answer was.
Play with these if you want but don’t fool yourself into thinking that you are a mental giant and others are idiots just because you got the joke first.