2 self driving vehicles are being tested. Both vehicles are exactly the same. Both are fitted with a camera on the Dashboard, although in car A it is a slightly older model and is 1 kg heavier than in vehicle B. The M25 is 117 miles long. Vehicle A started 2 mins before vehicle B and they both crossed the line within 60 seconds of each other. Why is this?
$\begingroup$ Are we assuming an imaginary line that you cross after driving all the way round (117miles), or is this a trick - there are no actual lines across the M25, and if there were, you wouldn't have to drive 117miles to get to the next one? $\endgroup$– Michael KayNov 12, 2019 at 0:35
Why is this?
Because that's the way traffic works. It's nothing to do with the weight of the cars, nothing to do with them being driverless, nothing to do with the age of the vehicles or whether they have dashcams, and nothing to do with the fact that it's the M25. Your journey time on a congested motorway is almost entirely decided by factors outside your control. The only decision you ever make is which lane to go in, and your decision is as likely to be right as wrong, so you're going to get random fluctuations in journey time.
1$\begingroup$ Not sure if it's just me... but I do feel that my decisions are more likely to be wrong... $\endgroup$– WhatsUpNov 28, 2019 at 22:40
I'm pretty sure the solution to this puzzle relies on the fact that:
The M25 is a circular motorway going around London. Note therefore that since in England cars drive on the left-hand side of the road, a car travelling anti-clockwise along the full length of the M25 would travel a slightly shorter distance than a car travelling clockwise, due to it travelling the whole distance on the inside track of the circle as compared to travelling on the outside track.
I'm no physics expert as to how much a 1kg difference in weight affects a car's speed, but I am inclined to think that:
The weight difference can be considered negligible and the difference in times is explained entirely by Car A travelling clockwise in the outside lane (thus travelling a longer distance), while Car B was travelling anti-clockwise on the shorter inside lane. Inevitably, Car B makes up some time on Car A.
If the 1kg difference does have an effect, then there is no need for the cars to be travelling in opposite directions on this circular motorway (or on a circular motorway at all, since the time difference effect could be achieved on a straight motorway through whatever the weight-related physics dictates), hence I am inclined to believe the above is the true puzzle-worthy scenario...
1$\begingroup$ Sebz gur dhrfgvba, pne o zhfg unir pnhtug hc ng yrnfg bar zvahgr ba pne n. Nffhzvat n pvephyne ebnq, gur gbgny yratgu bs gur vaare naq bhgre ynarf jvyy bayl qvssre ol gjb gvzrf cv gvzrf gur qvssrerapr va enqvhf. Gur ynarf ner hayvxryl zhpu zber guna 25z ncneg, zrnavat gung gur bhgre ynar vf nobhg 150z ybatre guna gur vaare ynar. Ng abezny fcrrqf ng n zbgbejnl, fhpu n fznyy qvssrerapr va qvfgnapr pna abg rkcynva gur pngpuvat hc. $\endgroup$– jarnbjoNov 11, 2019 at 18:03
$\begingroup$ @jarnbjo You've never driven round the M25, have you ;-) See Bass's answer for a more realistic description of its traffic - you definitely cannot assume a constant speed of 70mph (often you're lucky to do 5...) so my answer isn't as farfetched as the maths might make you think! $\endgroup$– StivNov 11, 2019 at 18:54
2$\begingroup$ If the motorway is 15m wide, then the outer edge is 30m longer than the inner edge, which is .00015 of the length - totally insignificant. $\endgroup$ Nov 12, 2019 at 0:43
$\begingroup$ No, never driven on the M25, but if your answer should hold, the average speed may not exceed 5.6 mph and it would have taken 21 hours to do the round. I do not believe that to be realistic. $\endgroup$– jarnbjoNov 12, 2019 at 11:41
1$\begingroup$ I didn't attempt to decipher your first comment, which appears totally cryptic. The difference in circumference between two circles of radius r and r+15m is 2π(r+15)-2πr = 30π = 94m. Yes, sorry, I was a bit out, but 94m of distance does not account for 1 minute of extra time. $\endgroup$ Nov 12, 2019 at 14:45
This makes use of Stiv's observation above, but develops it differently.
The extra weight of car A does make a small difference to its speed, but not a considerable one. This means that car B does over time catch up with car A. However, in order to pass car A, it has to pull out into an overtaking lane and is now actually driving a slightly longer route due to the M25 being circular and car B now travelling in a circle of a slightly larger diameter. This cancels out the slight advantage of weight and Car B is unable to overtake.
This does assume though that the M25 is perfectly circular, which it is not.
I believe the answer is that:
the cameras have a different frame rate.
Conclusions considered and excluded
There is a possibility this sentence ("The M25 is 117 miles long") is a non-sequitur placed into the question to throw us off, since it's completely unrelated to anything elsewhere in the problem. I'm going to assume not, though.
The M25 now has variable speed limits that depend on traffic, so even if it were empty, the speed limit could raise as the first one passes, permitting the second to catch up. I don't think this is the answer, though.
The vehicle in the lead will encounter more wind resistance; the trailing one will encounter slightly less due to a slipstreaming effect, so will be able to accelerate faster, and if speed is not limited, will also be able to travel faster. The slight extra mass of the camera in the lead car will also slow down acceleration and braking. The course is round, but this isn't a foot race so there's no reason they'd drive in different lanes unless one was overtaking: both will take the racing line. I don't think any of this is the answer, though: they give a result that's too vague, and leave too many details in the question unused.
Assumptions must be made
So I'm gonna assume that the two vehicles are alone on the M25 (an expensive experiment!).
Since this is clearly a timed race, they will, being self-driving, be driving as fast as they can, within the criteria (which we aren't told) of the race, and will travel the same path unless something makes them not do so.
It's likely that the M25 was picked specifically because at its theoretical top speed of 70mph (though it now has variable speed limits that depend on traffic), it takes almost exactly 100 minutes to do a lap. So if we have a laptime difference of 1 to 3 minutes, then there's a difference of 1% to 3% in the lap time between the two cars. The cars weigh more than 100kg, so the mass of the camera can't be to blame.
I note that the wording of the puzzle allows the second car to actually get in 59 seconds before the lead car, as well as merely gaining a minute against that car. In fact, by using "minute" in the description, they could start as far apart as 2:59.
The inevitable conclusion
I think the answer lies in that...
the camera is older, which might give it a different frame rate. Specifically, the UK uses PAL encoding (24FPS) rather than NTSC (30FPS). Older cameras that weigh a lot are likely to be movie cameras, though, which record at 25FPS.
And given that the car uses AI,
if the AI is poorly written, it might be using the distance traveled between two frames to calculate velocity, and if the race criteria are "stick to the legal speed limit" then it might think it is going slightly faster than it really is.
And, it should be noted,
24FPS and 25FPS are 4% different.
If car A starts at 1:00:00, car B starts at 1:02:59 then it leaves "2 mins" later. After a little under 100 minutes, car B crosses the line first, at 2:40:00 and car A crosses at 2:40:59... having lost 4 minutes out of 100 to the other car ...or 4%.
This answer uses all the question details
- the precise length of the M25 is 117 miles;
- its in the UK;
- motorways in the UK have a max speed of 70;
- the cars are both using AI
- one camera is older than the other
- one time was specified in minutes and the other in seconds
- the maximum time difference from the specification is a shade under 4 minutes.
The only thing I didn't use was the 1kg, and I think that might have been a red herring to distract from the real answer.
Since this is depicted as a real-world situation, I'll go ahead with the most likely real-world solution:
They started at
a time and place with relatively light traffic, that is, only a couple of other cars between them.
then, as it often happens,
they reached the tail end of a traffic jam.
Therefore, the front car would be driving very slowly while the rear car caught up.
Since there were
only a few cars between them,
the cars would end up quite near each other.
Incidentally, this is the exact same reason why there's always such a rush
of race cars taking a pit stop whenever the pace car is on the track.
they started at different locations!
2$\begingroup$ There's no lateral-thinking tag, so please refrain from such answers: it's trivial to invent a dozen silly answers like this, and none of them really adds anything to the puzzle. $\endgroup$– BassNov 12, 2019 at 8:08
1$\begingroup$ The question leaves so many assumptions open (e.g., were the cars actually on the M25?) that we clearly aren't supposed to read it at face value. $\endgroup$ Nov 12, 2019 at 14:56
They never mentioned that velocity(magnitude) of both car is same. Their velocity(in magnitude) would be different in order to follow that situation.