I normally post these on Friday, but the happiness project has taken over my life, and so I decided to post the puzzle today.

I try to vary the puzzles as much as possible, both in terms of how hard they are and the skills needed to solve them.  This one is from my colleague Mike, and is a tad trickier than most…..

As part of a rather odd driving challenge you are required to complete two laps of a racetrack at an overall average speed of 80mph.  At the instant you finish the first lap, you are informed that your average speed over that first lap was
only  40mph.  How fast do you need to travel over the second lap to get your
overall average speed up to the target value of 80mph?

The answer to this puzzle, and 100 others,  can be found in a new kindle ebook called PUZZLED, and is available in the UK here and USA here.

1. Venn Diagram says:

Think I’ve got this figured. 🙂

Just signed up for the happiness project – feeling pretty happy about it.

2. Seems like simple algebra equation to me..? Took about 30 seconds.

1. chloe says:

me too. i’m suspicious about that…

3. I’ve seen a variation on this before. This is gonna stump a LOT of people…

1. Exactly. It stumped Einstein’s friend “Bucky” when they sat together and calculated this … so they are in good company.

2. I should say “caught-out”, not “stumped”.

4. fairly easy – the trickier puzzle would be one where there is a fixed distance, but then it took x minutes to complete the course, how much faster for the remainder to meet the overall average speed…

5. Justin says:

Fairly straightforward algerbra. Took around 30 seconds, plus another minute checking there wasn’t a trick in the wording.

6. mslifeandsuperpowers says:

I got it in under 10 seconds, I hope =)

7. I thought I had the answer immediately, then thought through it again and realized I had it completely wrong the first time.

8. Mchl says:

One second for intuitive answer, then 1 minute analysing if I was right 😉

9. Raja says:

high school kinematics 😛

10. Mchl says:

Oh! And try to solve this, when one lap is exactly 40miles long (or even longer) 😛

1. Raja says:

Distance doesn’t matter my friend LOL

2. After dismissing the obvious answer as too easy, that’s exactly where I went next. As I’m sure you realise, I now have an exploded brain. I was going to assume that the answer would remain the same regardless of track length, but your comment makes me think otherwise.

11. fpilot says:

Beleive it or not I was taught this in primary school about 58 years ago. Even today I find most people I ask get it wrong.

12. Nick Sharratt says:

Took a guess after 30 sec that proved wrong. Took about a minute to do the algebra and got an answer that initially confused me thinking I’d messed up, about another minute to throw in some numbers to understand the question, then another 2 minutes to re-do the algebra on a slightly different basis which gave the same answer which then seems obvious as the right answer. Much longer than usual to feel sure I’ve got the right answer but feel like it took me much longer than it should have now.

13. Kevin says:

30 seconds for the simple calculation. But another minute to think through as many of the reasons for it to be wrong: e.g, by the time the communication was made you have already progressed on part of the lap at around 40; what the limits of G-force on the body mean – instantaneous acceleration from 40 to N would kill you – but is the need for a live driver at the end part of the puzzle?

14. I hope I have it right. Took about a minute, but figured I must’ve cocked up somewhere. Took a few more to re-check.

15. Will says:

The only workable answer I can come up with involves driving a Delorian.

1. ATravelller says:

Same here!

2. MarkB says:

How fast does it have to go before we get to see some serious shit?

16. JD says:

I think I got this in moments but like all of these puzzles I have self-doubt. Still, I’m in a happy mood anyway for some reason.

17. The first answer that seems obvious popped up right away, but the more mathematical mind dismissed that. The rest is just algebra.

18. Mchl says:

@Kevin: We’re talking average speeds here, so no problem with accelerations and such.

19. Victor Meldrew says:

About 30 secs, plus another minute or so to double check.

20. Maybe a minute? As DigDug said, it’s simple algebra although I like Will’s suggestion of using a Delorian.

1. Wondering if we move the experiment into space, and use gravity wells and the speed of light we can invoke some relativistic effect?

21. Notatheist says:

Thought I had it right, read the comments, re-read the question, now I have it right and I was wrong the first time.

22. thethreelimes says:

I went for the obvious answer first but re-checked and got a different answer. I was worried that I’d made a horrible mistake but from the comments of others I think I may have the right answer.

It took me just over a minute to get what I think is the right answer.

23. Alan James says:

Got it. My initial guess was way off, but a minute or so later, and a different approach, got me to the truth.

24. Took me about 5 seconds. These are the sort of SAT questions (well, they wouldnt actually put a trick question on there like this) that people waste their time on.
Very simple algebra.

25. Well, I got an answer in about 20 seconds, not sure if I was on the right track though *groan*

Came across you in twitter re the happiness experiment, glad to be part of it, though I am generally happy most days 🙂

26. Notatheist says:

I’m still waiting to find out what the happiness experimetn is really about. I’m skeptical of the claims made about it’s true purpose. ;^)

27. It’ll take some very serious gear shift work to get this to happen.

28. Notatheist says:

like I said, happiness experiment*

29. Pete says:

I arried at an answer in about 1 min by thinking about an eg lap of 80 miles. Answer seemed a bit odd so thought about it for another 2 or 3 mins, but sticking with original answer.

30. I got it in ~10 seconds, but these comments are starting to make me think I’ve gotten it wrong 😦

I’m with Jamie. Seems straight forward to me, although I can imagine an answer that many might jump to first, then realize a mistake.
I’m going to stick with the answer I came up with almost immediately.

32. Gib says:

Got it in 10 seconds…

33. AAAGHH!!! Yeah that’s a horrible one. Got the right answer now, but I had a helping hand. I can see a lot of people getting this wrong (me included :]).

34. Simon Perry says:

Got it before I finished reading it.

35. Bit confused by this. 20 minutes and a spreadsheet later and I’m with the ‘answer’ I got after 30 seconds, but think I still must be missing a trick….

36. Wilf says:

Nice puzzle you’ve got here Richard. Initially I was worried about the answer I’d got, but I keep checking it and I’m sure there’s nothing wrong with my thinking.

37. Helen says:

Got an intial answer in about 20 seconds, realised that I was probably wrong given that it’s supposed to be ‘a tad trickier than most’, so thought it through with a pen and paper. It took me a minute or two but I think I’ve got the correct answer now.

38. Rebecca says:

I’ve come up with an answer almost instantly, but I’m almost certain it’s wrong!! I’ll keep thinking about it and see if I can work out the correct answer!

39. Benjamin says:

Hooray for middle school maths. About 15 seconds.

40. JerWah says:

I am extremely happy to report 42 seconds.

41. Rebecca says:

OK, I’ve thought about it a bit more, and I’m almost certain I have the right answer. When I first worked out this answer I thought it had to be wrong, just because it seems so, well, weird, but I did a few more scribblings and that was enough to convince me it was right. This is a really interesting puzzle, the answer was so unexpected, and counterintuitive even.

42. Gus Snarp says:

I know why this is tricky will have to go back to my statistics notes to get the solution.

43. scott says:

20 seconds.

44. Matt says:

I wrote the equation and ground it out using high school algebra. Took about 30 seconds or so. I suppose there is a trick to get it immediately, but I haven’t figured that out yet.

-Matt

45. Austin says:

less than a minute, but i was distracted by being at work and doing work things.

46. Austin says:

also, hooray for the subie rally car. sexy.

47. TS says:

About half a minute and I would be the man to do it because I am The Stig. 😉

48. jimmeh says:

I can’t do it. I fail.

49. I got it extremely quickly, but by “it” I mean the wrong answer. I’m still not quite sure how to get the right answer so put me down for a long, long time.

50. Anonymous says:

Got an intuitive answer but, as always, reading the comments puts me off and makes me think it’s wrong…

51. faye says:

you’re kidding, right? It cannot be this easy ….

52. rolak says:

nice try, but I think I solved it almost instantaneous 🙂

53. Bucket says:

I got it really quickly as well, but I have a feeling I may have gotten it wrong, as it is supposed to trickier than usual…

54. Got it, took about a minute. Poor guy…

55. Hal Steinman says:

Took about a minute to interpret algebraically and solve. Then another two minutes to interpret the answer physically and accept its truthiness.

56. fpccraig says:

I’m having a slow brain day, so I had to take it back to my old friend distance = rate x time. Once I got the answer, I remembered having seen this problem before.

57. Got it pretty quickly – under a minute

58. Neil R says:

If i’ve worked it out right, it’s brilliant…if I’ve worked it out wrong, it’s brilliant!

It’s made me think, though…what if I am driving my car, and (forgetting speed limits- I’m on the Autobahn!) I need to average 80 mph to get to my destination on time. Then I find, when I’m halfway there, that I’ve only averaged 40 mph…wouldn’t anyone put their foot down?

59. Martin says:

Less than a minute.

60. Vero! says:

no me gustan esos autos

61. Vero! says:

Está bien..en 20 segundos

62. Michael K Gray says:

About a minute using logic to confirm my intuition (which occurred to me in ‘ flash’, as it were), and a further 30 seconds to verify it using algebra.

63. Michael M. Butler says:

I got stuck. Let it simmer for about ten minutes while I did something else. Came back and worked out an answer in about 30 sec.

64. An answer came to me before I’d finished reading, almost as intuition, but I’m not convinced that Mr Wiseman would post such a simple algebraic problem… not solved it yet (well, not to the point I’M convinced I’m right).

65. Kevin says:

I got my answer instantly as I read it, although I started to doubt it and looked at an alternative for a few mins. I couldn’t find one so stuck with first one.

66. Sally says:

I think that I have an answer. Took a few minutes.

67. Alan James says:

Richard it might be handy to have all these puzzles tagged or categorised under puzzle so we can easily go look through the old ones.

I enjoyed this one and now want more.

68. holysole says:

An algebra problem, took me roughly 30 secs to figure it out!

69. Anonymous says:

0

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Though i am weak in these things but i want to enhance my logical skills and so i joined this forum. i hope my desire will get fulfilled.
Thanks

71. Johnsticles says:

Easy as pie. that’s a simple Algrebra 1 equation!

72. Ditto to Ginny re: posting the earlier letters for new subscribers. Alsocan you explain to us who wrote the January letters?

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