# Why Does Almost Everyone Get this Question Wrong? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [April 21, 2020, 12:52am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239 "2020-04-21T00:52:17Z")\ **Posts on this page:** 20\ **Page:** 5
**Author:** ![AnalogSignal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/analogsignal/32/1085_2.png) [@AnalogSignal](https://boards.straightdope.com/u/AnalogSignal)\ **Post date:** [April 22, 2020, 10:55pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/81 "2020-04-22T22:55:13Z")
> [@TriPolar](#): > > 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. It’s easier to understand by looking at this [graph](https://www.wolframalpha.com/input/?i=plot+2%2F%281%2F15%2B1%2Fx%29%2Cx%3D0..100000). The X axis represents the average speed of the downhill trip. The Y axis shows the average speed of the entire trip. By increasing X, you can get Y to 29.9999999 but it never hits 30. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [April 23, 2020, 1:43am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/82 "2020-04-23T01:43:42Z")
> [@TriPolar](#): > > 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. I always always tell my kids to put units on their equations. That Wolfram Alpha equation, with units, looks something like this: 2 miles, divided by the sum of two discrete fractions of an hour [one fraction representing how much of an hour it takes to go the first mile, and the second representing how much of an hour it takes to go the second mile], is equivalent to 30 miles divided by one hour. Each discrete fraction represents traveling one mile (the numerator) divided by the speed per hour (the denominator). That’s still hella chunky, but it gets us started. If you want to divide two miles by some fraction of an hour and show that’s equivalent to thirty miles an hour, you need to divide it by 1/15 of an hour, because at 30 MPH you go 2 miles in 1/15 of an hour, or 4 minutes. So the sum of the two discrete fractions must equal 1/15. One of the fraction is already 1/15, so the second fraction must equal zero. But there’s no fraction with a numerator of 1 that equals zero. It’s crazy to me that some people understand it easier with equations than with the narrative I wrote several posts back, but I know different brains work differently. ---
**Author:** ![jackdavinci](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackdavinci/32/3259_2.png) [@jackdavinci](https://boards.straightdope.com/u/jackdavinci)\ **Post date:** [April 23, 2020, 2:03am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/83 "2020-04-23T02:03:12Z")
[quote=“TriPolar, post:78, topic:852239”] 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. [QUOTE] Ok maybe I was just tripping over the wording of the original explanation. So 3 chickens would lay 6 eggs in 3 days. I can buy that angle. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 23, 2020, 2:19am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/84 "2020-04-23T02:19:10Z")
> [@Left\_Hand\_of\_Dorkness](#): > > It’s crazy to me that some people understand it easier with equations than with the narrative I wrote several posts back, but I know different brains work differently. The narrative is definitely simpler but it only explains why you can’t average 30 MPH. It’s a lot more difficult to work out the equation that would produce an answer if the car did the first mile a little faster. I certainly don’t have the patience for that, I’m that kid in your class staring out the window by now because who cares about Einstein’s crappy old car anyway? ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 23, 2020, 2:20am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/85 "2020-04-23T02:20:29Z")
> [@](#): > > Ok maybe I was just tripping over the wording of the original explanation. So 3 chickens would lay 6 eggs in 3 days. I can buy that angle. Just remember that old saying, “An apple and a half in a day and a half keeps one and a half doctors away.” ---
**Author:** ![penultima\_thule](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/penultima_thule/32/3833_2.png) [@penultima\_thule](https://boards.straightdope.com/u/penultima_thule)\ **Post date:** [April 23, 2020, 3:09am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/86 "2020-04-23T03:09:41Z")
> [@TriPolar](#): > > It’s a lot more difficult to work out the equation that would produce an answer if the car did the first mile a little faster. Actually it’s not: To average 30mph over a two mile course the trip must be completed in 4 minutes. So you calculate the time in minutes for the first mile. The return speed is simply 60 divided by the residual time in minutes. So: Up @ 30mph takes 2.0 mins so Down is 60/(4.0-2.0) = 30.0mph Up @ 25mph takes 2.4 mins so Down is 60/(4.0-2.4) = 37.5mph Up @ 20mph takes 3.0 mins so Down is 60/(4.0-3.0) = 60.0mph Up @ 17.5mph takes 3.43 minus so Down is 60/(4.0-3.43) = 105mph Up @ 15mph takes 4.0 mins so Down is 60/(4.0-4.0) = undefined/impossible Up @ 15.1mph takes 3.9735 mins so Down is 60/(4.0-3.9735) = 2,265mph ---
**Author:** ![AnalogSignal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/analogsignal/32/1085_2.png) [@AnalogSignal](https://boards.straightdope.com/u/AnalogSignal)\ **Post date:** [April 23, 2020, 4:36am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/87 "2020-04-23T04:36:07Z")
I agree with **Left Hand of Dorkness** ’ verbal summary. To state it in terms of formulas, you are being asked to solve for x: 2/(1/15+1/x)=30 where x represents the speed of the car downhill. This equation can be simplified further as solve for x: 1/x = 0 There is no solution because no matter how large x gets, 1/x is always greater than 0. ---
**Author:** ![Melbourne](https://avatars.discourse-cdn.com/v4/letter/m/b5e925/32.png) [@Melbourne](https://boards.straightdope.com/u/Melbourne)\ **Post date:** [April 23, 2020, 9:06am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/88 "2020-04-23T09:06:24Z")
> [@TriPolar](#): > > How did you and they buy things in the old days when everything used to cost a nickel? You paid sixpence. At Coles Variety Store: " 3d, 6d and 1’ store. Nothing over 2’ " That’s pence and shillings. The d in LSD comes from denarii, as in librae, solidi, denarii (or libra, solidus and denarius). From Old French Latin, from the Norman conquest of England, from the English colonization of Australia. ---
**Author:** ![MarvinKitFox](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@MarvinKitFox](https://boards.straightdope.com/u/MarvinKitFox)\ **Post date:** [April 24, 2020, 6:22am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/89 "2020-04-24T06:22:01Z")
> [@Ynnad](#): > > Almost everyone I ask gets this wrong. Engineers, accountants, and physicists all get it wrong. They all insist that the cheap pencil costs 10 cents. Even when I show them they are wrong, they still insist that the cheap pencil costs 10 cents. Sorry, but you know some very stupid engineers, accountants, and physicists then. In a recent similar question, with even the same values used (but a different object), some 92% of highschool kids and 97% of college students got the answer right. Either that, or you are fumbling the question in some way. Deliberately, maybe, to show your “superiority” to the people being asked? Try the same question, asked the way you asked it here. In writing, with simple and direct language. You will be amazed at how the percentage of correct answers changes! TL;DR: It’s not the question, it’s not the questioned. It’s the questioner. ---
**Author:** ![road\_lobo](https://avatars.discourse-cdn.com/v4/letter/r/d78d45/32.png) [@road\_lobo](https://boards.straightdope.com/u/road_lobo)\ **Post date:** [April 24, 2020, 9:09am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/90 "2020-04-24T09:09:16Z")
> [@Ynnad](#): > > What is it about this question that almost invariably invokes the wrong answer. There is no hidden trick or misleading information. What is going on here? People can tell it’s a riddle, not a serious question, so they zone out and do a lazy calculation to humor you. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [April 24, 2020, 12:42pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/91 "2020-04-24T12:42:41Z")
> [@MarvinKitFox](#): > > Sorry, but you know some very stupid engineers, accountants, and physicists then. > In a recent similar question, with even the same values used (but a different object), some 92% of highschool kids and 97% of college students got the answer right. These are really specific numbers. Are you thinking of a specific experiment, and can you link us to these results? I find them surprising. ---
**Author:** ![yarblek](https://avatars.discourse-cdn.com/v4/letter/y/71e660/32.png) [@yarblek](https://boards.straightdope.com/u/yarblek)\ **Post date:** [April 24, 2020, 1:11pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/92 "2020-04-24T13:11:41Z")
For my own amusement as a mathematically challenged dummy and for anyone so or otherwise inclined: Going up a hill at 30 mi/h and going back down at 60 mi/h, it seems obvious that the distance does not change going up and down the hill. So if you know this, an average speed of 45 mi/h can never be correct even if I really felt like it should have been. It might be easier to see this when assuming a value for the distance but I wanted to solve it without doing so algebraically. [ol] [li] Average speed is total distance/total time. [/li][li] Total distance is up hill + down hill = x mi + x mi = 2x mi.[/li][li]Total time = (distance going up hill / speed going up hill) + (distance going down hill / speed going down hill) [/li]= (x mi / 30 mi/h) + (x mi / 60 mi/h) = (2x mi / 60 mi/h) + (x mi / 60 mi/h) = 3x mi / 60mi/h = (3/60)x mi / mi/h = (1/20)x / h.[/ol] Therefore, the average speed = 2x mi / (1/20)x h = 2(20) mi/h = 40 mi/h. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [April 24, 2020, 1:23pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/93 "2020-04-24T13:23:28Z")
Here’s a report on doing this test at various institutions [https://pubs.aeaweb.org/doi/pdf/10.1257/089533005775196732](https://pubs.aeaweb.org/doi/pdf/10.1257/089533005775196732) . 7% of MIT students got **none** of the three questions (which included the ball/bat (or “pencil”) test) right. ---
**Author:** ![yarblek](https://avatars.discourse-cdn.com/v4/letter/y/71e660/32.png) [@yarblek](https://boards.straightdope.com/u/yarblek)\ **Post date:** [April 24, 2020, 1:32pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/94 "2020-04-24T13:32:44Z")
Oh by the way, this problem made me think of the [Wason selection task](https://en.wikipedia.org/wiki/Wason_selection_task). The vast majority of individuals fail this task even if the answer is “obvious”. Can people who make claims in this thread that most (intelligent) people would or would not be able to solve the problem in the OP actually have any good source of data that shows this? Would be interesting to know. Why so many posters in this board love to share their anectodes is a mystery to me. Edit: I see Andy L posted something already! ---
**Author:** ![yarblek](https://avatars.discourse-cdn.com/v4/letter/y/71e660/32.png) [@yarblek](https://boards.straightdope.com/u/yarblek)\ **Post date:** [April 24, 2020, 1:50pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/95 "2020-04-24T13:50:49Z")
> [@Andy\_L](#): > > 7% of MIT students got **none** of the three questions (which included the ball/bat (or “pencil”) test) right. And only 48% got all questions right. The group at Princeton had only 26% that got all of them right (the second highest in the study). ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 24, 2020, 2:35pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/96 "2020-04-24T14:35:36Z")
> [@MarvinKitFox](#): > > Sorry, but you know some very stupid engineers, accountants, and physicists then. … You are absolutely correct in that assessment. Their stupidity amazes me sometimes. ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 24, 2020, 2:39pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/97 "2020-04-24T14:39:17Z")
> [@MarvinKitFox](#): > > S …Try the same question, asked the way you asked it here. … I asked the question exactly as stated in the OP. But not in writing. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [April 24, 2020, 2:48pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/98 "2020-04-24T14:48:29Z")
> [@Andy\_L](#): > > Here’s a report on doing this test at various institutions [https://pubs.aeaweb.org/doi/pdf/10.1257/089533005775196732](https://pubs.aeaweb.org/doi/pdf/10.1257/089533005775196732) . 7% of MIT students got **none** of the three questions (which included the ball/bat (or “pencil”) test) right. > [@yarblek](#): > > Oh by the way, this problem made me think of the [Wason selection task](https://en.wikipedia.org/wiki/Wason_selection_task). The vast majority of individuals fail this task even if the answer is “obvious”. > > Can people who make claims in this thread that most (intelligent) people would or would not be able to solve the problem in the OP actually have any good source of data that shows this? Would be interesting to know. Why so many posters in this board love to share their anectodes is a mystery to me. > > Edit: I see Andy L posted something already! These two links are both really interesting. Thank y’all! > [@Ynnad](#): > > You are absolutely correct in that assessment. Their stupidity amazes me sometimes. What do you think they would say about you, were I to ask their opinion of you? ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 24, 2020, 2:53pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/99 "2020-04-24T14:53:57Z")
> [@Left\_Hand\_of\_Dorkness](#): > > … What do you think they would say about you, were I to ask their opinion of you? They would say I am stupid. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 24, 2020, 3:02pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/100 "2020-04-24T15:02:55Z")
> [@yarblek](#): > > Oh by the way, this problem made me think of the [Wason selection task](https://en.wikipedia.org/wiki/Wason_selection_task). The vast majority of individuals fail this task even if the answer is “obvious”. This illustrates my point about “Who cares about John’s pencils anyway?”. People have very little invested in answering a random test question. It would have been interesting to see what happened if the subjects were offered payment for a correct answer. Or in the case of students reward them with some points on their GPA. [Previous page](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239.md?page=4) [Next page](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239.md?page=6)