Speed Race: Newsletter Challenge (April 2013)

It seems to me, that if they pass each other three times, the only pass that matters is the third, back at point A.

If the speeds are constant, and they cross at the exact starting point on the third lap, the minimum speed of car 1 is 50 mph, same as car 2. It's also the maximum speed and the average speed.

The drawing is important, but is not to scale. It clearly shows more distance CCW from A to B than CW A to B. Let's put some numbers to it, say 50 miles between each letter. Car 2 is moving at 50 mph, so it takes 1 hour. Car 1 can get there in one hour by going 100 mph, but it can also go 250 mph and get there at the same time as car 2. That (250 mph) also works for crossing C and then A at the same time. 100 mph is the minimum of 100 and 250, so that's the answer.

We could be really picky and stipulate that it must be either a figure eight track or a two level track to avoid one car having to travel further in the outer lane.

According to data and drawing, every third crossing happens at point A. If the B and C points are positioned in the order we see in the drawing, is enough to conclude that Car 1 ends two rounds at the same time Car 2 ends 1, ie Car 1 speed is 100mph, plus points A,B,C, divide the "track" into three equal lengths. S.M.

2 times the speed of car 2 equal 100mph at constant speed!

there are 3 meetings of the cars for a full turn!

first meeting is at a third for car2 and 2/3 of car 1; second meeting is at 2/3 for car 2 and 4/3 of car 1 and the third meeting is at a full round for car2 and 2 full rounds for car 1!

Also car 1 drives at the same time the double way of car 2 and this is equal the double speed!

if car 1 stops while racing the maximum speed must be higher!

Points A to B the short distance, measured 76 mm on my monitor's screen.

Points A to B the long distance, measured 129 mm.

Changing that to 7.6 km and 12.9 km respectively, I calculate the unknown speed to be 85 mph.

All this assumes that the first time the cars pass each other is at point B, but the question is ambiguous. It doesnt say the first time the cars pass each other asthat could happen many times on the track, just not at point B. The question could be read as the first times both cars pass each other 'at point B', meaning they could pass each other many times outside of their stated points A, B, and C. It's only AT THESE points that they pass one time, two times, and three times.

As usual, this is a poorly formulated Newsletter Challenge that does not say what is invariant and what is not. As shown, the answer is 100mph, but if the order of A-B-C can change, the answer is 25mph. (As already mentioned.)

CR4 really needs to get somebody to vet this stuff; nearly every such Challenge has something wrong with it.

CR4 does have some one to vet these - us! :O

Too little too late!!

I find that sorting out the challenges provides much more entertainment than the solving of the challenges themselves.

Also, it takes many of us, a few posts before we isolate the problem; I think CR4 would have to hire a posse of engineers to review the challenges before offering them.

I like it the way it is.

Yes lets go back to....

If you turn on your headlights at light speed will you see the illumination ahead of you?

the cars meet first at point B and they are travelling at constant speeds

by this reasons the time for the race needed is:

t=(l1+l2+l3)/v2=(l1+l2+l3+l1+l2+l3)/v1=2(l1+l2+l3)/v1

and so v1=2*v2

l1=A-B

l2=B-C

l3=C-A

Maybe after almost 100 responses, an answer from the question poser with their explanation is timely.

In the real world, there comes a time to make a decision, push the package out the door and save any incremental changes/improvements for the next model. I think that time has come to this "Speed Race: Newsletter Challenge".

Can I offer one more scenario?

Let's cpnsider a ratio of the two cars' speeds.

And consider these givens:

Total distance = D, Car 2 speed = 50mph, first meeting is at B, second is at C, cars leave going in oposite directions. X = The speed of C2

Therefore, the distance between A and B is equal to the distance between B and C.

So C1 travels D + D - 2AB which reduces to C1 travels D - AB at Xmph

and C2 travels 2(D - AB) traveling at 50mph.

The ratio then becomes: 2(D - AB) : D - AB = X : 50

This solves out to 100 which would be the speed of C1

So the answer is 100mph

Agree ... 100mph. See my answer #15.

Others have come up with the same answer, for a range of reasons.
We may all be wrong ... time for the answer and no doubt some vital detail
we missed in the fine print so we will learn to be more observant.

Rethink the problem, but totally ignore the picture of the egg-shapped race track. The diagram is wrong and misleading.

Just approach the problem as a word-only problem and you will find there are only two possible solutions and the correct one of the two will be obvious.

Cleaned up the last of the (Easter) egg, whirled my whiskers,
(which is not bad being cleaned shaved), and peered again at the small print ...

Two cars start moving in opposite directions from point A.
OK, 2 cars start at the same point, point A.
The 2 cars are heading in opposite directions.

They are traveling at constant speeds on a closed race track.
Assume wrongly (?) that there was instant acceleration to that constant speed.
And 'they' suggests both are on a closed track.
Do we assume that they are on the same closed track or are they on different tracks?

The cars cross for the first time at point B, then at point C, & a third time at point A.
The 2 cars cross for the third time at the start point A.
If the track for one car was 'flat' and the track for the second car
was any shape but flat ...
like progressive lines of longitude tracking on a sphere ...
to achieve the crossing points,
the minimum distance would actually be a line of latitude ...
two laps of ... in the same time.
Is this where I go wrong?

If the speed of Car 2 is 50 mph, what is the minimum speed of Car 1?
If the speed of one car is twice the speed of the other car ...
then for the MINIMUM speed,
it is NOT 100mph as previously said (#15 etc) but actually 25mph,
as the speed 50mph is the speed of the car travelling at twice the speed
of the other car.

Agree .... there are 2 answers 25mph compared to the 50mph of Car 2
or 100mph compared to the 50mph of car 2 ...

For the MINIMUM, then the other car speed is 25mph.
(Thanks Anonymous Hero .. a lesson in reading the fine print!)

If Car2 is traveling at 50mph and meets Car1 at point B, and both leaving in opposite directions, there is no way Car1 can get to point B which is one third the distance of the course if he is only going half the speed of Car2. He has to be going twice the speed of car 2 in order to accomplish that fete because he has traveled twice as far in the same time, so he must be going twice the speed.

Forget the picture that is given with the puzzle. It is wrong.

Points A, B, and C are not as described in the picture.

I believe the picture IS relevant as it determines the relative position of the FIRST passing point. If it is as drawn then the speed is, as you said, 100 (2x car 2). For car 1 to be travelling at 25 B & C would have to be reversed.

P.S. I'm using Firefox and can't select any other emoticons. I never thought such a trivial thing would annoy me.

I think there is significant evidence that the picture was added as an afterthought.

The reasoning goes like this:

1. The problem asks for the minimum speed for the other car, which implies there is more than one possible solution to the problem.

2. The problem is solvable without a picture.

The likelihood that a word problem would be structured such that point #1 is irrelevant is less likely than the likelihood that the addition of the picture is wrong, given that the picture is unnecessary and confounds the problem in the first place.

Firefox is my browser of choice too! And look ... it is possible to be cool
Just left click on in the menu strip and you get a choice of 16! I hope that removes one annoyance.

Talking of 'reverse' ... see my #118 suggestion. I changed my minimum speed from 100mph (twice the speed) to 25mph (half the speed) and even 12.5mph (technically -12.5mph) if one of the cars was travelling in reverse, effectively going in the same direction but facing in the opposite direction as the other car. All answers fit the words and the pic.

Quite right Don, I cannot remember now how I originally got that answer. But it is a possibility that first came to mind. 12.5mph

Hi Jacko, my first attempt #15 was the 100mph outcome, but on reflection, there needed to be another answer ... hence the 25mph and then 12.5mph. We will see what the almighty poser of the q's decides on.

If you want another challenge ... look at the CR4 interchange on high speed rail in Taxifornia. Where it has local interest, is the announcement today about the $100+ Billion high speed rail between Brisbane via Sydney and Canberra to Melbourne.

http://cr4.globalspec.com/thread/83091?frmtrk=cr4sd#newcomments

take a track on the surface of a cylinder, than the tracks can be parallel and there's no difference in the length at the meeting points.

It is that 1 car has to be going half the speed of the other. The distances have to be equal between the points or the speeds will not be constant to make the third pass at the point of origin. The total amount of laps completed by both cars cannot be anything other than 3 or they will not pass 3 times. The shape of the track is about as relevent as the make of the cars or the names of the drivers. It is 2 cars going opposite directions, and meet at the beginning for the third pass, nothing more.

Here's another thought: Car 2 is the only one bound by the "givens". He must go 50mph. Car1, on the other hand can vary his speed as he has not been required to do follow any speed restrictions. It only asks what is the minimum speed that he must ravel to accomplish the meetings as shown. However, if he chooses to drive at 200 miles for a short distance and then wait for Car2, his minimum speed could drop to 0mph during his waiting period. He could actually drive backwards for a short distance and then speed up to catch the meeting point. So, it appears the answer could be that there is no minimum speed because he could, in theory, speed up to whatever speed required to make up the "down time" if you will. Interesting?

From the original puzzle post, "Two cars start moving in opposite directions from point A. They are traveling at constant speeds..."

They key is the word "They", which explicitly implies both cars are traveling with constant speed.

You are absolutely right. I missed that. I now go back to my post #106. The answer is 100 mph. Thanks, again.

or 25 mph it does not state that the car doing 50 is the slowest car does it?

The word problem says nothing about which car is slower. Only the diagram, which is largely discredited, implied that Car 2 was slower through the relative positioning of points B and C.

I see and you are correct. If car 2 was not the slowest car they would meet closer to point C first, B second, and A last.

Discredited by whom? - a bunch of Jacks with no more insight than your own.

The diagram was submitted as part of the question, why should it not be taken as true?

It was once said that -"Given enough time, enough Typewriters and enough Monkeys, they would eventually reproduce the works of Shakespeare.

I think that this Forum, and especially this thread, has discredited that theory beyond any doubt.

The original WORD problem was submitted sans diagram on the GlobalSpec website. It says they are BOTH moving at constant speed in opposite directions around a closed course. It doesn't say it has to be a perfect circle. It doesn't say to account for the width of the track or allow for the possibility of the track as being a Mobius strip. It doesn't say that one or both of the cars could be speeding up or slowing down. It says they are both moving at constant speed. It doesn't say which car is going clockwise. It doesn't say which car goes the longest way around the track to get to point B.

The salient points to extract from the text of the problem are these:

1. Two cars start moving around a closed track in opposite directions at constant speed from a designated point A.

2. They meet twice at two other points, B & C, on the track before meeting again at the first point at which they had met.

3. One of the cars is moving at a constant speed of 50 mph.

The only question that seems valid to me is, did they both instantly start moving at the constant speed of 50 mph in the case of Car 2 and the unknown speed in the case of Car 1 which is a physical impossibility in the real world but not impossible in a thought experiment. The words strongly imply that they both instantaneously started moving at constant speed from point A. Any other consideration makes the problem insoluble without more information.

Given the assumption of instantaneous acceleration to a constant speed in opposite directions on a closed track (doesn't even have to be circular), then passing each other twice before meeting again at their origin (point A), one of the cars had to have traversed the track twice and the other once. Given the constant speed specification, they would have had to have met at two points 1/3 and 2/3 around the track from point A. Anything less than 2/3 and greater than 1/3 would not have resulted in meeting at the exact same starting point after meeting twice before. If the distances around the track to point B were identical, then their next meeting would be at point A and their speeds would both be 50 mph. If they met at 3 intervening points prior to meeting again at point A, the speed of Car 1 would have been 150 mph or 50/3 mph (16 and 2/3 mph).

By the way, if the track were a Mobius strip and gravity wasn't an issue, the correct answer would still have been 25 mph for Car 1 as both cars would eventually meet at point A with a ratio of 2 times around the tack for one of the cars and once around the track for the other.

It says they are both moving at constant speed.

So there is NO ACCELERATION or SLOWING DOWN to be considered.

It doesn't say which car is going clockwise:

The ARROWS SHOW clockwise and anticlockwise....!

both cars travel at a constant speed, car 1 at 50 mph, given in the challenge..

G'day Commoner. Read the question carefully, it states that both cars travel at "constant" speed.

Just another 2c worth

A 'final' out of left field answer ....

What if the 'slower car' faced away from the faster car but was actually travelling at constant speed ... in reverse. It is a car that no doubt has reverse gear. The speed of the slower car is 12.5mph. (-12.5mph for the pure among you, which is definitely less than 100mph, 50mph, 25mph and even if stopped). And that fits with the picture.

A "negative speed" for Car 1 is ruled out by the condition that the cars leave in opposite directions. As soon as you add a negative to a speed, you're no longer working purely with the rate of increase of the path length, but are actually working with a vector and implying a direction, even if that direction is not clearly defined. In this case of this puzzle, the direction of Car 1 is defined only in a relative sense, ie opposite to the direction of car 2. So when you add a negative to the speed, the effective direction pops back around and the cars are no longer going in opposite directions.

if both cars leave in the same direction than car1 runs at four times the speed of car2 for travelling A-B-C-A and it runs at 5/2=2.5 the speed of car2 by travelling A-C-B-A.

By the reason of constant speed the distances between A-B-C are constant too!

At the point of being even sillier than some of the responses- here are two more- since the track is circular both vehicles are returning to the start point so the distance traveled in a specific direction is zero- except for the fact that both the earth and universe are also travelling at two varying speeds from the big bang point and therefore the distance traveled and resultant speeds should take those velocities into question.

100 MPH

it does not say how wide the track is. Both cars could snake and zig-zag, or go in a series of reverse loops within the width of the track- or go straight(ish)- all at constant car speed.

Car 2 goes 'straight' at 50 mph. Car 1 'zig-zags' at constant speed within the width of the track (the track has width to allow cars to pass). Car 1 must do 2 laps to that of Car 2, but being slightly longer laps it must go a little more than twice as fast by a zig-zag factor. The minimum speed will however be 100 mph if it does not zig-zag.

Alternatively, Car 2 zig-zags at 50 mph, and Car 1 goes 'straight', in which case for Car 1 the two laps are slightly less than twice the lap of Car 2. The speed will therefore be less than 100 mph - the minimum depending on the degree of zig-zag.

Interestingly, I wonder, for smooth running, would the path of the zig-zag tend to trace out a sine wave or a series of alternating half circles.

The constant is time. So if car 2 travels 2/3rds of a lap (50mph) and car 1 travels 1/3rd of a lap.

Pass @ Point B

Repeat this so car 2 has traveled 4/3 rds laps and Car 1 has traveled 2/3rds of a lap,

Pass @ point C

Repeat this so Car 2 travels 6/3 rds laps and Car 1 has traveled 3/3rds.

Pass @point A

To achieve this Car 2 is travelling at twice the speed of Car 1 i.e Car One is going at 25 mph.

you've changed the car numbers!

Unknown: precise distance between points

Assumption: distance between points is equal but still unknown.

Based on information given and the assumption, Car 1 must travel at least 100 mph.

Consider this ..... the speed of one car is twice the other car ....
so 100mph is twice 50mph, but if one car is travelling at 25mph and the second car is travelling at twice the speed at 50mph, then that also fits the criteria ... so 25mph is the minimum.

It is self apparent that one car must travel two circuits of the track while the other travels one and that the cross over points A,B and C are equidistant. The key to this question is the reference to the MINIMUM speed of car 1.

We do not know which is the faster car, so we must assume car 1 is the slower and therefore car 1 will be travelling at 25 mph. If it was the faster of the 2 cars it would travel at 100 mph, both answers satisfy the question but car 1 travelling at 25 mph meets the requirement of MINIMUM speed.

Mike McA

BRAECO1

Some additional thoughts on "negative speed":

Understanding speed to be the positive magnitude of a vector velocity, then speed, strictly speaking, cannot be negative. We can, however, interpret "negative speed" as a positive speed in the direction opposite to that indicated.

So, if only one of the cars moves at constant positive speed with a negative direction (relative to the arrows on the diagram) then both cars are going in the same direction and that is not allowed by the problem statement. However, if both cars move in a negative direction relative to their respective arrows, then they are moving in directions opposite to each other (meeting the stated conditions) and thus (again referencing the illustration) Car 1 is able to move with a lower speed than Car 2 to reach point B at the same time as Car 2.

Some have said that the illustration is irrelevant. However, the composer does not say that. Therefore, if we consider the illustration as "given", Car 1 will travel in the direction of its arrow and Car 2 will travel in the direction of its arrow. Further, the writer states that "...the cars cross for the first time (emphasis mine) at point B, then again (my emphasis again) at point C..." Therefore, if Car 2 travels to the right as indicated by the illustration, and Car 2 is traveling at 50 mph, and we have proven that either Car 2 is twice the speed of Car 1 or it is half the speed of Car 1 the following must be evident: Car 2 will traverse one third of the track by the time it meets Car 1, and (see given) if next meeting is at point C, it has gone the exact same distance it travelled and in the same amount of time to reach point C from point B, while Car 1, if traveling half the speed of Car 2, would meet Car 1 at point C first, not point B. Their next meeting, then, would be at point B with the final meeting being at point A. Therefore, if we follow the directions to the letter, the speed of car 1 must be twice that of Car 2 = 100 mph.

Respectfully, neither does the composer of the problem explicitly (or implicitly) say that the illustration is actually relevant, or more precisely, to what degree the illustration is relevant.

We're interpreting a challenge which falls in the genre of "brain teaser word problems" which, in my experience beyond this forum, will typically refer to a diagram explicitly if dependent on it - otherwise it is often an illustration added to make an editor happy.

Further, we have already determined that the physical spacing of the marked points on the drawing is not relevant, due to inconsistency with the requirements of the word problem. (the requirement of constant speeds) So the image is already not 100% relevant.

The directional information given on the image constrains the problem to a single solution, and thus the written requirement that we select the minimum of possible solutions become degenerate, and its inclusion is unnecessary. I (and others) argue that this is inconsistent with the genre, where typically only the minimum amount of relevant information is given, and therefore the marked direction of travel and/or the relative order of labelling for the points A, B and C is also not relevant to the solution, and has instead become a red herring.

If you discount this argument you are required to take either the position that the minimum constraint on the solution is then a red herring either designed to put us off the trail to the solution, or that the composer of the Challenge was not careful about choosing the problem constraints. If you take the first position, okay, that is your weighing of the probabilities. As for the second position, I think it is unfair to the person who submitted the problem to presume that they did it wrong because you don't like the way they presented the challenge. By all means presume them malicious - it's a challenge after all! - but being wrong needs to be proven by the provided solution.

All this said, if this challenge was intended to be written and interpreted in the genre of "poorly written engineering specification", then I think no one is correct except the people who have offered tentative solutions but indicated the need for clarification from the person who submitted the challenge.

OK. The answer is, if Car 2 goes to the right as shown on the drawing, and he travels at 50 mph, and Car 1 goes the opposite direction he will travel 100 mph to accomplish the requirements of the puzzle. If, however, Car 2 goes in the opposite (left) direction, and Car 1 goes in the other direction (right) he will travel at 25 mph to make the puzzle correct. Therefore, there are two answers: If the direction of travel for the two cars is as shown on the drawing, the speed of Car 1 is 100 mph. If the travel is opposite that shown on the drawing, Car 1 is going 25 mph. I am betting the composer wants 100 mph. We'll see.

As previously raised, if the 'opposition directions' is also regarded as a red herring, as the cars may face in opposite directions, but actually travel in the same direction, (the drawing being regarded as being a further red herring and the term 'speed' is used and not 'velocity', where velocity means speed AND direction), then the minimum speed is now 12.5mph to fit with the 'guidance and crossing notes'.

The question states that the cars cross paths, not that car one passes car 2 at given points. The question is what is the minimum speed. the answer has to be 25 mph.

You are correct

Oliver Dunthorne

2 correct answers I believe. Twice as fast or half as fast. 100mph or 25mph.

And the MINIMUM speed answer is ..... ?

This is very simple: There are 3 variables from this and only one unknown. The fundamental speed=dist/time formula. Now the time from start t finish is the same for both cars, obviously. Both cars are running at constant speed. Speed of car#2 is known (50mph). We can see from the question that car#2 makes one lap at this speed, and also that car#1 makes 2 laps, obviously faster. Time being equal for the race, we have (let dist=d and speed for car#1=$):

d/50=2d/$

That means car#1 speed is 100mph.

The question asks for "Minimum speed"

Well then, that would be the minimum speed, since it was stipulated that the cars run at constant speed (no acceleration/deceleration).

Accepted that one car is travelling twice the speed of the other car ...
but what if the 50mph speed was the speed of one car,
which is twice the speed of the other car ....
so the other car is travelling at 25mph ...
Hence the minimum speed of a car is 25mph.

Calculations were based on distance rather than speed, and that based on the assumption that the distance along the path between the points is equal, and Car 2, travelling at 50 mph, will have to travel 1/2 the distance of Car 1 in the same amount of time in order for both to reach point B at the same time.

If the speed of Car 2 is 50 mph, what is the minimum speed of Car 1?
If the speed of one car is twice the speed of the other car ...
then for the MINIMUM speed,
it is NOT 100mph as previously said (#15 etc) but actually 25mph,
as the speed 50mph is the speed of the car travelling at twice the speed
of the other car.

There has been some discussion about the importance / errors of the diagram.
I believe that it is agreed that one car is travelling at twice the speed of the other.
If one car is travelling at 50mph, then for MINIMUM speed, the other car travels at 25mph.

According to the diagram given showing the direction of travel for each of the cars, and based on the assumption that the distance is equal between points, Car 2 has a shorter distance to travel to point B than Car 1, starting from point A. If Car 1 is traveling at 25 mph from point A in the direction shown, and Car 2 is traveling at 50 mph from point A in the direction shown, then Car 1 would only be halfway to point C at the time Car 2 reaches point B.

See answer #119 and consider the suggestion of Anonymous Hero ...
Back around #15, I thought the 'other car speed' was 100mph,
but that just gets you thinking about the question.

"I think there is significant evidence that the picture was added as an afterthought.

The reasoning goes like this:

1. The problem asks for the minimum speed for the other car, which implies there is more than one possible solution to the problem.

2. The problem is solvable without a picture.

The likelihood that a word problem would be structured such that point #1 is irrelevant is less likely than the likelihood that the addition of the picture is wrong, given that the picture is unnecessary and confounds the problem in the first place."

Yes. Moreover, in classical geometric problems, one is NOT supposed to rely on any diagrams, unless the wording explicitly states what is shown. Some of Euclid's geometry goofed because of not keeping track of the order of points on a line or arc.

Unfortunately, we don't know what this Challenge's poser really intended as far as what should be relied upon.

The only way that can happen is to totally ignore the diagram. In that case, IF Car 2 is going counter clockwise at 50 mph, then Car 1 going clockwise at 25 mph will cause meetings at Point B, then Point C and back at Point A in tha order. OR

IF Car 2 is going clockwise at 50 mph, as shown on the diagram, and Car 1 is going counter clockwise at 25 mph, as shown, they will meet at point B, then point C and back at point A ONLY IF the locations of those points is chronologically counter clockwise. That is if C is located where B is shown on the diagram and B is located where C is shown on the diagram and the diagram, again, is ignored.

IF we take the diagram to be gospel, then the answer has to be 100 mph for Car 1.

Given that this is a closed race track, I assumed that the direction of the A_B_C points would be in a counter-clockwise direction (race track standard direction). Since the direction of the cars is not specific, I chose the direction of car 2 to be travelling 50 mph (clockwise), and car 1 to be travelling counter-clockwise. Which gives car 1 a relative speed of 25 mph. (not much of a race track with speeds from 25 mph to 100 mph and you can drive in whatever the hell direction you want) This is why clarity with the specifications is a critical issue. (-2,+2) , a^2=4

The answer is more confusing than the original question. Is Car 2 moving at 50 mph or 100 mph? In the drawing, Car 2 is moving from point A to Point B at 50 mph. If that is the case, then Car 1 must be moving at 100 mph or twice the speed of Car 2. Ya gotta keep your cars straight. I'm out of here!

So what if you discard the picture ... which, as suggested by some, was added later? I guess it somewhat depends on your exit speed and which car you have your money on?!

"The cars cross for the first time at point B. " The (2) cars are travelling in opposite directions.

1. Car 1 travels from A to B. Car 2 travels from A, past C, and then to B, where it crosses paths with car 1 for the first time.

2. Car 1 travels from B to C. Car 2 travels from B, past A, and then to C, where it crosses paths with car 1 for the second time.

3. Car 1 travels from C to A. Car 2 travels from C, past B, and then to A, where it crosses paths with car 1 for the third time.

We are back at point A in two laps. Car 2 is travelling twice as fast as Car 1 (in my example). Given Car 2 is travelling at 50 mph, Car 1, therefore is travelling at 25 mph.

The example clearly does not indicate that Car 2 travels for A to B. It says..... "The cars cross for the first time at point B."

My example does not indicate there is much of a race. (25 mph and 50 mph) I am not saying 100 mph is incorrect. I am saying that, the way in which the example is written, and without a diagram, an awswer can be derived another way.

It seems that the real question is "are diagrams relevant in a specification?" Does it make a difference if the said diagram is a 'generic' drawing. e.g. A concrete footing, a fillet weld on a flange or a motor wiring placard that then conflicts with the written word. Then again what if the diagram is bespoke to the description but appears to conflict that description, as in this puzzle. Are there any legal requirements to follow one or the other? Assuming that the conflict can't be cleared with the author. Is there a convention that I don't know about?

Jim

If the points are clockwise, in order of A,B, C. and car 2 has to travel twice the distance to reach the first point of intersection and again twice as far to reach the second point of intersection, then car 2 is traveling twice the speed of car 1. If car 2 is 50 MPH, then car 1 is 25 MPH.

the second half of the answer said:

"If car 2 travels at a speed given by 100n mph, where n are a positive integer, the cars will also meet at point B for the first time. Therefore to meet at the three given point in the order specified, the minimum speed of car 2 must 100 mph, or twice the speed of car 1."

Is it just me, or is that contradictory gibberish?

Also note that this is the first mention in either the problem statement or the answer that the order of the points is actually described as being specified by the drawing, rather than the drawing simply demonstrating a solution.

This is the last Tues of the month. I look forward to seeing the answer...along with an explanation.

Is it just me, or is that contradictory gibberish?

It's not just you it is complete gibberish! Even if you allow for the fact that they've mixed up car 2 and car 2 (sic.) the n*100 mph solution just does not work in any way.

If the speed of car 2 is 50 mph in the question, but must be 100 mph in the answer. I give up, the solution is don't waste time on these questions.

One car is travelling twice as fast as the other. Since there is no way of telling which is faster, if car 2 is travelling at 50 mph then car 1 is travelling at either 25 mph or 100 mph [these are the only possiblities] so the minimum speed of car 1 is 25 mph and the maximum is 100 mph.