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.

[davebro]

If the out was 1 hr, & 330 miles the return would take 2 hrs. So it flew for 3 hours & covered 660 miles. 660/3 = 220 av speed.

[bhg481]

dave - it might not be obvious to georgina that 165mph is EXACTLY half 330mph, it takes twice as long to get back as to get there because it is flying at half the speed.

[davebro]

Incidentally the fastest helicopter made is a Sikorsky & tops out at 299 mph. So the one in this example must have been wind assisted on it's outward run & against the wind on return.

Roughly speed 250 + 80 mph wind = 330 mph
250 - 80 mpf wind = 170 mph
(can't be bothered to work out the fractions!)

[AuntPollyGrey]

The question does not say what the length of the journey is. The helicopter could have taken anything from 5 minutes to 5 hours to complete its journey at 330mph. So the distance is variable.
In my opinion the answer is wrong (unless we have not had the correct question.) I'm sure someone can do a calculation on paper but I would have thought that the answer would be ( 330 + 165) / 2 = 245.5.

[bobbinwales]

it would be the same answer whether the distance was 1 mile, 100 miles or 20000 miles Aunt Polly. As bhg explained the key is that the return is same distance but takes twice aslong

[davebro]

Sorry APG - length of journey is immaterial & your calculation is wrong.

[ToraToraTora]

the length of the journey is irrelevant, that's the point of the question, to realise what are the salient factors, this is not primarily about the arithmetic. The journey back always takes double the journey there, let's call the distance D, the average speed A and the Time T, so the total journey takes 3T thus: A=2S/3

[bobbinwales]

yes Torra, altho you meant 2D/3??

[THECORBYLOON]

"S" is used to represent distance so that velocity (v) equals distance/time or s/t.

[ToraToraTora]

no 2S/3 twice the speed the distance is irrelevant. so 660/3. we take the proportion the speed back is of the speed out and divide it to get the adjustment factor in this case 330/165 = 2.

[Ellipsis]

> let's call the distance D, the average speed A and the Time T, so the total journey takes 3T thus: A=2S/3

bobb was pointing out that you called it "D", not "S", Tora ...

[Ellipsis]

davebro's first post shows the intuititvely obvious way to do this. The working in full is shown below:

Speed = Distance / Time, i.e. S = D / T

Journey 1:
330 = D / T
therefore D = 330T

Journey 2:
165 = D / t2
where t2 is the time for the second journey, and D is the same distance as the first journey
therefore t2 = 330T / 165
So t2 = 2T

Average:
Speed = (Distance out + Distance back) / (Time Out + Time Back)
S = (D + D) / (T + 2T)
= 2D / 3T
= 660T / 3T
= 220

[Curiousgeorgina]

Ok, I done some of my own work now. The common factors is 1 and 2.
X1x330=330
X2x165=330
X3=660
X=660/3
X=220

[Curiousgeorgina]

All of you are right, but also wrong because if we change the numbers and the speed is not double then wouldn’t work. I found an other example from Mensa where same scenario the numbers are: 590mph and 393.33 respectively.

[bobbinwales]

of course it wouldnt work if the speed wasnt double. Not sure why that make sus all right and wrong. That would of been a diffrent question and a diffrent answer

[Peter Pedant]

av speed is not an average of speeds !
it is total distance over total time

it is one of the things you can do reelly well wivva matrix

speed-distance-time and then fill in and total as needed

[davebro]

1 HR AT 590 = 590 MILES return takes 590/393.33 = 1.5 hrs

So 1180 miles takes 2.5 hrs Av speed = 1180/2,5 = 472

Don't think any helicopter would achieve that but maybe the form of transport is also immaterial!

[bobbinwales]

Yes. A remembeer a problem like this from night school
http://www.ibankingfaq.com/interviewing-brainteasers/a-car-travels-a-distance-of-60-miles-at-an-aveage-speed-of-30-mph-how-fast-would-the-car-have-to-travel-the-same-60-mile-distance-home-to-average-60-mph-over-the-entire-trip/#:~:text=Most%20people%20say%2090%20mph,hours%20(120%2F60).

[Peter Pedant]

no it does work - fill out the matrix -

speed dist time
330 x x/330
165 x 2x/330........ total dist 2x, total time 3x/ 330
divide one by the other and it is 220 QED

[bobbinwales]

We all allready agreed on that Peter.