First, if you live in the Coventry area, I am performing and speaking at the lovely Albany Theatre on the 18th Match. Do come. Details here.

So, the puzzle. Please do **NOT** post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

You drive to your office at 20 mph and return by the same route at 30 mph. Discounting the time spent at the office, what was your average speed?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle **(UK here and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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Mean, Mode, or Median? I get three different answers.

Mean. That’s the definition of “average”.

Assume a round trip of 120 miles, ie 60 miles each way.

This would take 3 + 2 = 5 hours

So the average speed is 120 divided by 5

Note: I did not post the answer

It took me about 1 minute to come to various possible and valid answers š

Ken, both mode and median are “averages”. The mean is just colloquially accepted as the only average worth discussing, doesn’t mean the others aren’t still averages.

There is only one correct answer to “average speed”. And it is not the obvious answer.

I can only imagine the most obvious answer, which I got in a couple of seconds. Look forward to the answer on Monday. (Re. Stu’s comment: wouldn’t the mode and the median be the same in this case?)

Me too, Anne.

WARNING – I’m just replying here to let anyone know who is scrolling down the comments, that a few comments down “ashish shah” has posted an answer, despite being asked not to. My lips are sealed as to whether it’s right.

PS. The answer is 24

Now that a couple of windowlickers have posted the answer, I can see that my own comment about the mode and the median being the same is total nonsense.

Ten seconds plus another twenty mulling it over to make sure I had not made a mistake.

Average Speed = 24 mph

Average stupid comment rate so far: 33.3%.

Did you read the instructions?

Well, that is the obvious answer – one assumes there is some sort of catch, however – that would just be too easy.

Lord Manley,

That’s good to hear my liege, but we were hoping that you might have two answers, one of which did not require capitals, like you did in December.

I did?

Link?

No, it can’t be as simple as think it is.

My thoughts exactly, Charles; but I can’t tweezer out any more information (hills? wind speed? friction? – that kind of thing). So I’ll have to stick with the obvious one. I’m intrigued by that “ashish shah” twat’s comment, I must admit.

Some might consider the information I refer you to as a spoiler.

If you want to understand his comment, read the 1st paragraph of the Wikipedia entry on “speed”.

The post above was intended to be a reply to Anne Elk.

Thank you, Beanfeast; that’s kind of you. Unfortunately, I’m such a maths div that I still can’t get a different answer!

“A surprise critical and commercial success, it won two Academy Awards, for Best Sound Editing and Best Sound Mixing at the 67th Academy Awards in 1995.”

Took the most obvious guess in about 2 seconds, decided it was too obvious in 5 and stepped through the maths in a couple of minutes.

20 seconds to do the maths

Similar problem: If it is 1 mile up a hill and it takes you 2 minutes to go up (that is at a speed of 30 mph) then at what speed must you come down again to average 60 mph?

Obviously I am faster going downhill, even at the same speed. So your trick question’s answer is 30mph going down too.

Starting to think that RW ought to close comments to all of the Friday Puzzle posts. It serves no purpose to have hundreds of people stating “took me two seconds” and far too many are posting the answers.

Half of friday’s puzzle is ‘doing it in two seconds’,

then the other half is spotting who has the wrong answer.

Wrong answers include base17, 25 and Schopenhauer.

I think these “pre answer” comments are enjoyable. I work on the problem before looking at comments. It took me about 30 seconds, a bit longer than I expected. I was disappointed that I had to resort to a pen and paper.

What would Monty Hall say?

mgm75

If you do not like the comments functionality, why are you using it?

Keep ’em coming, Hugh!

Hear here (re comments) + similar http://home.mathsshare.com/Lists/Team%20Discussion/DispForm.aspx?ID=18&Source=http%3A%2F%2Fhome%2Emathsshare%2Ecom%2FLists%2FTeam%2520Discussion%2FAllItems%2Easpx&RootFolder=%2FLists%2FTeam%20Discussion

pen & paper, 1 minute.

Straightforward algebra. I’m going to carry on looking for a neater way to do it though.

You’re not given a distance, and the distance shouldn’t matter – so you can just pick a nice example number that makes it easy to calculate. Say the office is 60 miles away, then you can do the maths quickly in your head.

Hey, thatās how I did it too, chosing 60 miles š

Got the obvious but wrong answered immediately. Had to read the comments for a clue to get the right answer. I know it mathematically works, but would like to understand (without using maths) why the obvious answer doesn’t even though it seems like it should.

<<>>

He travelled longer doing 20 mph than he did doing 30.

That intuitively explains why the answer is closer to 20 than to 30.

But the obvious answer *is* the correct answer. The answer which i got instinctively within a fraction of a second is the correct one which i calculated to check.

Spent a minute puzzling over the wrong method, then the right way to do it just popped into my head.

Although ashish shah jhas correctly given the “right answer” based on some assumptions, we do not yet have enough information to know for sure.

Is my drive to work the same distance in each direction? “One way” systems, especially roundabouts make this unlikely even for many simple joineries of the sort that are used to create puzzles.

If for example we say that the Journey Home (as in Star Trek Voyager where they had to drive through the entire Delta Quadrant after being balckholed there outwardly) is 30% longer than the drive to work, we arrive at a different answer at all together.

… Plus road conditions for each journey, wind speed and direction, tyre pressure, traffic light sequences, radio station being listened to, making a phone call whilst driving (illegal I hasten to add), astrological birth sign, weight of driver during each stage, what he/she had for lunch, state of alertness of driver, whether or not the driver’s boss is is my father’s son, the current situation in North Korea, Jose Mourinho, blah blah blah.

It took about half a second to get the answer instinctively, and then about 15 seconds to check it by calculating it properly.

I was going to say the same but it sounded too smug š

30 seconds, as I was also pondering how it could possible be as simple as it sounded. And then I remembered that that man’s father is my father’s son.

This was a very different question if he had asked about velocity intend of speed.

It would?

Please elaborate or give the answer if the question had been “about velocity intend of speed” – on Monday of course – we don’t want any spoilers do we?

This is a pretty standard algebra problem. One minute, including the calculations by hand.

I think I go to the answer to fast for it to be true. Can’t be that simple.. well anyway looking forward to Mr Wiseman cleares things up.

About 2 minutes (since my algebra is very rusty). Had to create a scenario.

I would like to see your performance, Richard. When is the 18th Match?