Mensa Question Here.

[Curiousgeorgina]

A helicopter covers its outward journey at 330 mph. It returns over exactly the same distance at 165 mph. What is the helicopters average speed over the entire journey? The answer is 220, but how? I got these cards fun, but some are really hard! Thank you for your answers.

[Etch]

If the 2 speeds (to cover the same distance) are S1 and S2 then the general formula is:
Average speed = 2 x S1 x S2 / (S1 + S2)

[AuntPollyGrey]

Just to clarify, in my original reply I did say that the distance was variable , meaning it did not matter in the equation and was irrelevant. Something obviously got lost in translation.

[Curiousgeorgina]

Bobin, I was hoping for a unified theory. :) Sorry Tora, I missed your reply, yes, the factors. The answer for the second is 472mph.

[bobbinwales]

We allready have a unified theory is average speed = total distance divided by total time

[Curiousgeorgina]

Bobin, I am sorry, I am bit slow ;) First time posting, maybe missed something.

[bhg481]

Curiousgeorgina - was the answer you gave from the answer book or did you use Etch's formula?

[Curiousgeorgina]

Davebro, how did you get 1180? Please.

[bobbinwales]

Etches formula is all you need for a 'unified theory'

[bobbinwales]

georgina- davebro got the 1180 by adding 590 and 590?

[bobbinwales]

^ distance there an back using your example of traveling 590 miles each way

[Prudie]

Never heard of it, can't google it. What is Etch's formula (or the alternative spelling of Etches)?

[bhg481]

davebro ASSUMED the first flight took 1 hour so, at 590mph it must have been 590 miles. The return flight is the same distance, so total distance travelled is 590 + 590 = 1180 miles.
The time for the second flight is 590/speed = 590/393.33 hours.
Total time is 1 hour + 590/393.33 hours to travel 1180 miles.

[bhg481]

Prudie - Etch is an AB user who provided a formula at the top of page 2 of this thread.

[Curiousgeorgina]

Oh! :) No I see Bobin. The other way is much simpler.
I was trying to take
2x*590=1180
3x*393.33=1180
5x=2360
x=2360/5
x=472
Thank you all.
The questions are from Mesna 60 Questions cards 2016.

[Prudie]

Oh the poster Etch!!!
Someone on previous page gave the clear formula for working out average speed. It's total distance divided by total time. It works easily in this example only because obviously speed one way was exactly double the other so there are 3 lots of the same time to do the whole journey.

[AuntPollyGrey]

// Someone on previous page gave the clear formula for working out average speed. It's total distance divided by total time. //

Am I missing something here? Distance was not mentioned in the question, neither was the time the journey took.

[bhg481]

The actual distance doesn't matter. Mathematicians substitute a letter for the distance; others can just choose a random distance and work out the time of each trip using the quoted speed and that distance. You then get an overall time for the round trip and, hence, an average speed.

[AuntPollyGrey]

thanks! The light bulb has now come up to illuminate my brain cell lol!

It doesn't matter how long the journey was or what distance, as the average MPH will be the same whether the journey was 10 miles or 1000 miles, and it can be worked out using Algebra - kerching!

[Peter Pedant]

// We all allready agreed on that Peter.//
yes bobo BUT so often
there is note to my answer than the answer - - -
there is a 3x3 matrix nestling down there

also works for - - - density - mass - volume
p1 m1 v1 etc

( 2g of density 3.5g/ml and 5 mls of density 4g/ml makes a mixture of density what AND....
copes with what is the new density if there is an overall contraction of volume of 10% )

which I dont think - - - you agreed on

[Peter Pedant]

// Am I missing something here?//
yup me ( said that, not you must be missing me)

of dist, speed time - you only need two given to define the third ( two degrees of freedom BUT that is a bit advanced for 2' skool)

so if you do a speed - dist - time matrix
first part of the journey sp---d-----time and so on with the rows

you fill in all the spaces with the info given and then can sum it

here you have to realise that the Distance D or X is not given but so long as it is the same froo-out, it will cancel in this calculation

and I have to thank Mr Townend of Downside school for the matrix idea which he taught us in 1965