# Why do most people have trouble with this brain teaser? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [September 23, 2002, 5:00pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296 "2002-09-23T17:00:51Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![The\_Ace\_of\_Swords](https://avatars.discourse-cdn.com/v4/letter/t/e495f1/32.png) [@The\_Ace\_of\_Swords](https://boards.straightdope.com/u/The_Ace_of_Swords)\ **Post date:** [September 27, 2002, 3:47pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/41 "2002-09-27T15:47:42Z")
And divining the obscure is not any hallmark of intelligence? All I know is… ME MENTAL GIANT! ! HA! HA! RUN LITTLE PEOPLES FROM MY PUZZLE CRUSHING MIND!! Oh, damn, I think I fooled myself. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [September 27, 2002, 4:23pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/42 "2002-09-27T16:23:35Z")
> [@](#): > > 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. Well, actually I was being facetious (since you can’t travel the speed of light), and I am not a physicist, but it’s my understanding that if you _could_ travel the speed of light, _no_ time would pass for you. So you would complete the second lap in literally zero time, and complete both laps in two minutes. It’s also my understanding that if you _could_ travel faster than the speed of light, time would flow backwards for you–in doing that, you could actually average over 60 mph. ---
**Author:** ![Tiburon](https://avatars.discourse-cdn.com/v4/letter/t/e36b37/32.png) [@Tiburon](https://boards.straightdope.com/u/Tiburon)\ **Post date:** [September 27, 2002, 4:30pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/43 "2002-09-27T16:30:10Z")
Hm. I read what **Degrance** wrote and I have to respectfully disagree that asking a question like that posed in the OP is as bad as dropping rotten eggs on someone. Part of this is because I do not see asking questions like this as “practical jokes.” I like these riddles because if I get the wrong answer, I don’t assume it was the asker’s intention to make a complete fucking asshole out of me. I think it is just a fun little puzzle that you need to asked in order to appreciate. Lemme take a poll, though - Would you rather be asked more questions like that posed in the OP or have some rotten eggs dropped on you? Tibs. ---
**Author:** ![amarinth](https://avatars.discourse-cdn.com/v4/letter/a/3be4f8/32.png) [@amarinth](https://boards.straightdope.com/u/amarinth)\ **Post date:** [September 27, 2002, 4:34pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/44 "2002-09-27T16:34:00Z")
> [@](#): > > \*Originally posted by Degrance \* > \*\*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?” > \*\* What kind of physics classes did you take? Did the problems say “John traveled 3 miles in 2 hours, which averages to 1.5 miles/hour. What was his average velocity?” Given the rate and the distance, I expect a person to be able to figure out the time. I should not have to explicitly state it because it is right there. The question is phrased as any general 2 part problem, rate, distance, find the missing variable, use it and and the second distance to find the second rate. Basic algebra/physics. There is nothing hidden, there’s nothing tricky, and it is very simple math. I see nothing wrong with asking _graduate_ students to do that. I see nothing wrong at all in expecting that potential hires be able to do very basic algebra (but then, I work in tech). The useful information gained is that they’re able to work through a problem instead of jumping to a conclusion, and that they have that pesky multiplying thing down pat. Not a trick question at all. ---
**Author:** ![amarinth](https://avatars.discourse-cdn.com/v4/letter/a/3be4f8/32.png) [@amarinth](https://boards.straightdope.com/u/amarinth)\ **Post date:** [September 27, 2002, 5:01pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/45 "2002-09-27T17:01:36Z")
> [@](#): > > \*Originally posted by amarinth \* > **Did the problems say "John traveled 3 miles in 2 hours, which averages to 1.5 miles/hour. What was his average velocity?"** I need to amend this to say “John traveled 3 miles _in a straight line_…” ---
**Author:** ![RAWDuke](https://avatars.discourse-cdn.com/v4/letter/r/71e660/32.png) [@RAWDuke](https://boards.straightdope.com/u/RAWDuke)\ **Post date:** [September 27, 2002, 6:44pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/46 "2002-09-27T18:44:48Z")
> [@](#): > > 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?” So… we should make it easy enough so it’s no longer a “brain teaser?” This reminded me of the joke about “Math History” Teaching Math in 1950: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit? Teaching Math in 1960: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit? Teaching Math in 1970: A logger exchanges a set “L” of lumber for a set “M” of money. The cardinality of set “M” is 100. Each element is worth one dollar. Make 100 dots representing the elements of the set “M”. The set “C”, the cost of production, contains 20 fewer points than set “M.” Represent the set “C” as a subset of set “M” and answer the following question: What is the cardinality of the set “P” for profits? Teaching Math in 1980: A logger sells a truckload of lumber for $100. Her cost of production is $80 and her profit is $20. Your assignment: Underline the number 20. Teaching Math in 1990: By cutting down beautiful forest trees, the logger makes $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the forest birds and squirrels feel as the logger cut down the trees? There are no wrong answers. > [@](#): > > 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. Yaagghhhh!! Put me in the Monumentally Unpleasant catagory. Although…in the right situation…with the right person…maybe…Yaagghhhh!!! > [@](#): > > 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. I hope we can agree to disagree on this one. If you didn’t have all the information you needed to solve the problem, I would agree that it would be a “trick” question. Such as if this were multiple choice, and “this is not possible” were not one of the choices, I would be very irritated. However, everything you need to know is presented (except it’s assumed you have a basic math and english knowledge) ---
**Author:** ![ZooMetropolis](https://avatars.discourse-cdn.com/v4/letter/z/e480ec/32.png) [@ZooMetropolis](https://boards.straightdope.com/u/ZooMetropolis)\ **Post date:** [September 27, 2002, 7:22pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/47 "2002-09-27T19:22:54Z")
> [@](#): > > _Originally posted by Tiburon_ > > **Would you rather be asked more questions like that posed in the OP or have some rotten eggs dropped on you?** A: More questions… yes, more questions. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [September 27, 2002, 11:29pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/48 "2002-09-27T23:29:36Z")
Here’s the general solution, showing that it doesn’t matter how long the track is. Say the distance around the track is d. The time needed for the first lap is d/30 (units of furlongs per fortnight or whatever.) The time needed for two laps at an average of 60 mph is 2d/60 = d/30, exactly the same amount of time as it took to go one lap, so you’d have to do it at infinite (\> c) speed. As for travelling at the speed of light - it might work in the reference frame of the traveler, but not in the reference frame of the observer. Nice puzzle. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [September 28, 2002, 1:14am UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/49 "2002-09-28T01:14:03Z")
After a full day at work and a long commute, my brain is a bit frazzled. Let me get this straight: In order to average 60mph over two miles, you have to travel two miles in two minutes. (Assume instantaneous accelleration, since most of this sort of problem usually uses a “perfect system”.) Since you have used two minutes to go one mile, you have no time left to go the remaining mile. If you drove the second mile at 600mph, then it would take you six seconds, right? So you will have made two circuits in 2.1 minutes. That averages to about 57mph. Right? ---
**Author:** ![Dr.Lao](https://avatars.discourse-cdn.com/v4/letter/d/2bfe46/32.png) [@Dr.Lao](https://boards.straightdope.com/u/Dr.Lao)\ **Post date:** [September 28, 2002, 4:00am UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/50 "2002-09-28T04:00:56Z")
> [@](#): > > \*Originally posted by Johnny L.A. \* > \*\*Right? \*\* Yes, you are correct. And the question is not a trick. If you calculate average velocity the way you are supposed to (total distance travelled / total time) then it quickly becomes apparent that you cannot average 60 MPH over 2 miles if you travelled the first mile at 30 MPH. OK, maybe it is a little bit of a trick. ---
**Author:** ![Pabitel](https://avatars.discourse-cdn.com/v4/letter/p/bbce88/32.png) [@Pabitel](https://boards.straightdope.com/u/Pabitel)\ **Post date:** [October 1, 2002, 12:10pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/51 "2002-10-01T12:10:53Z")
> [@](#): > > \*Originally posted by Tiburon \* > \*\*Hm. I read what **Degrance** wrote and I have to respectfully disagree that asking a question like that posed in the OP is as bad as dropping rotten eggs on someone. Part of this is because I do not see asking questions like this as “practical jokes.” \*\* Just to be clear I intended this to be in regards to asking this type of question in an interview or other situation where one does not like to look bad, where some smug interviewer can sit and look down his/her nose at the object of their little amusement. In that case, yes, I would prefer the rotten eggs at least then the jerk couldn’t rationalize his objectionable activities. ---
**Author:** ![Pabitel](https://avatars.discourse-cdn.com/v4/letter/p/bbce88/32.png) [@Pabitel](https://boards.straightdope.com/u/Pabitel)\ **Post date:** [October 1, 2002, 12:18pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/52 "2002-10-01T12:18:07Z")
> [@](#): > > \*Originally posted by amarinth \* > \*\* There is nothing hidden, there’s nothing tricky, and it is very simple math. I see nothing wrong with asking _graduate_ students to do that. I see nothing wrong at all in expecting that potential hires be able to do very basic algebra (but then, I work in tech). The useful information gained is that they’re able to work through a problem instead of jumping to a conclusion, and that they have that pesky multiplying thing down pat. > > Not a trick question at all. \*\* The original question asks, “How fast do you have to drive the second lap in order to average 60 MPH for BOTH laps?” That is directly stating that there is a speed, a correct answer, at which this problem can be solved. When you build that assumption into the question then you are attempting to trick the person into thinking that there is a correct answer. There is not a correct answer. Therefore this is a trick question. Got it? ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [October 1, 2002, 12:52pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/53 "2002-10-01T12:52:23Z")
Want to watch me drive the second lap? Want to see it again? (old joke, I know) ---
**Author:** ![RAWDuke](https://avatars.discourse-cdn.com/v4/letter/r/71e660/32.png) [@RAWDuke](https://boards.straightdope.com/u/RAWDuke)\ **Post date:** [October 1, 2002, 1:07pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/54 "2002-10-01T13:07:52Z")
> [@](#): > > The original question asks, “How fast do you have to drive the second lap in order to average 60 MPH for BOTH laps?” That is directly stating that there is a speed, a correct answer, at which this problem can be solved. When you build that assumption into the question then you are attempting to trick the person into thinking that there is a correct answer. There is not a correct answer. Therefore this is a trick question. But there IS a correct answer. “It’s not possible” is a perfectly correct answer, and you are given everything you need in the original puzzle to reach this answer. You are tricking yourself when you assume something that’s not correct, and not implied. ---
**Author:** ![Mr.Cynical](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@Mr.Cynical](https://boards.straightdope.com/u/Mr.Cynical)\ **Post date:** [October 1, 2002, 1:24pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/55 "2002-10-01T13:24:43Z")
This is a math question designed to throw you off. Were it not, the question would ask if it were POSSIBLE, rather than how to do it. Deception + distraction = trickery. Is that easy enough for you guys to figure out? Sheesh. ---
**Author:** ![amarinth](https://avatars.discourse-cdn.com/v4/letter/a/3be4f8/32.png) [@amarinth](https://boards.straightdope.com/u/amarinth)\ **Post date:** [October 2, 2002, 6:57am UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/56 "2002-10-02T06:57:33Z")
> [@](#): > > \*Originally posted by Degrance \* > \*\* > > The original question asks, “How fast do you have to drive the second lap in order to average 60 MPH for BOTH laps?” That is directly stating that there is a speed, a correct answer, at which this problem can be solved. When you build that assumption into the question then you are attempting to trick the person into thinking that there is a correct answer. There is not a correct answer. Therefore this is a trick question. > > Got it? \*\* No. It doesn’t require any outside information, it doesn’t require that the solver do anything but set up the equations and solve the problem. You do the stated problem _exactly_ the same way that you would do the problem if you were calculating for an average speed of 57mph for both loops. Would that have been a trick question because the answer is 600mph rather than 84mph? The problem can be solved. And it can be solved the way that someone should expect to solve this kind of problem. This isn’t tricky. ---
**Author:** ![Gary\_T](https://avatars.discourse-cdn.com/v4/letter/g/3ec8ea/32.png) [@Gary\_T](https://boards.straightdope.com/u/Gary_T)\ **Post date:** [October 2, 2002, 4:56pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/57 "2002-10-02T16:56:07Z")
What makes this a trick question in some views is that it asks for something specific which cannot be provided. There exists no speed at which one can drive to correctly answer “How fast do you have to drive the second lap…”. By asking WHAT the speed would be, the question implies that there IS such a speed. The correct answer (it’s impossible) is not a response to the question actually asked, but to the unasked question of whether there is ANY speed at which it can be done. ---
**Author:** ![The\_Ace\_of\_Swords](https://avatars.discourse-cdn.com/v4/letter/t/e495f1/32.png) [@The\_Ace\_of\_Swords](https://boards.straightdope.com/u/The_Ace_of_Swords)\ **Post date:** [October 2, 2002, 5:46pm UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/58 "2002-10-02T17:46:53Z")
I agree, hence the second question I provided, which exactly the same percentage of people will get wrong, as the underlying math problem is what trips you up, though Problem A’s answer is annoyingly unsatisfying. Anyhow, are we moving on yet? Here, I’ll post another brain teaser in a new thread. -Ace ---
**Author:** ![psychobunny](https://avatars.discourse-cdn.com/v4/letter/p/54ee81/32.png) [@psychobunny](https://boards.straightdope.com/u/psychobunny)\ **Post date:** [October 3, 2002, 1:13am UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/59 "2002-10-03T01:13:07Z")
> [@](#): > > \*Originally posted by Horseflesh \* > \*\*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, to average 40mph you would have to drive the second lap at 60 mph.😃 ---
**Author:** ![ITzSmores](https://avatars.discourse-cdn.com/v4/letter/i/8e7dd6/32.png) [@ITzSmores](https://boards.straightdope.com/u/ITzSmores)\ **Post date:** [February 19, 2017, 7:14am UTC](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296/60 "2017-02-19T07:14:51Z")
You do the 1st lap in 2 minutes/30mph and you have to complete a total of 2 laps at this rate 2 laps would take 4 minutes and would be averaged at 45 mph to get an average of 60mph on the second lap you would have to do the second lap at 60mph cause 30+60/2 is equal to 60 aswell the laps are never said to be consecutive nor does it say he doesn’t build up speed until he hits 30mph and then keeps a steady speed for his first lap and if the laps aren’t consecutive then he could build up speed until he gets to 60mph after the first lap and then once he hits it steady speed for the second lap average those out and he drives an average of 60mph. Or you can take 45 break it into 3 get 15 and multiple that by the 4 minutes and get 60 for the second lap (btw you divide by 3 cause that’s how long the 2 laps would take) [Previous page](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296.md?page=2) [Next page](https://boards.straightdope.com/t/why-do-most-people-have-trouble-with-this-brain-teaser/129296.md?page=4)