How fast do I have to go?

BS.

Average speed

is specific terminology, it means precisely what it means,

oh, then enlighten us on what ELSE it means....

 

Squid: Your problem is that you imagine (uncritically) that you can average speeds. Speed does not work that way because it's not a pure scalar quantity. Speed is a distance divided by a time, and when you try to average speeds, you come up with wrong answers.

I half suspect, though, that you know you're talking bull, and you're just doing it to pull our legs.

It is depressing, however, that so few people can understand such simple mathematical concepts. No wonder we get the people we do in elected office, when the public does not know how to think critically.

 

Well, you are right. Average is average.

If you drive 1 mile at an average speed of 30mph, it will take you 2 minutes. No question.

If you average 60 mph over 2 miles, you have to drive the 2 miles in 2 minutes. No question.

But you spent 2 minutes driving the first mile. There is no way to catch up. No way, except, as pointed out, to hit the EV and drive at an infinite speed.

There is simply no other way to look at it.

 

I just wanted to comment on this part:

I think many can. However FEW like sitting around taking the time to solve questions as such.

But of course, I'm a contrarian, so don't listen to me.


h34r:

 

And, yea, what he said.

 

I think it took me no more than 20 seconds to figure this one out.

 

We'll send you your golden Prius trophy in the mail, please provide your home address.

 

I just did, actually, in the post you quoted. But if you don't believe me, feel free to google for it, or look it up in Wikipedia or even an English dictionary

 

i think squid is hung up on the difference between these two sentences:

"what is the average of the two speeds?"

and

"what is the average speed?"

or #1 stated in the context of this problem : "what speed must he go on the 2nd lap such that the average of the two speeds is 60MPH?"

squid is correct when he says that 90 is the answer, but that is the answer to question #1, not question #2. if you did 90 on the 2nd lap, the average speed is 2miles/(2minutes + 40sec) = 2mi/2.6666666...min = 2mi/0.0444444...hr = 45mph. efusco's argument is right, but its not 45sec @ 90mph, its 40sec.

 

No where in the problem does the sentence "what is the average of the two speeds?" appear.

Clearly, this sentence is an inferred, and even incorrecly inferred, question.

 

You will have to sent it to several other people who were a lot faster than me!

 

fair enough, i was just taking a stab at explaining why squid thinks his answer is correct.

 

Since this is FHOP and apparently high post count is a good thing...

This would also be 45 (mpg). Average is total distance / total gallons.

1st mile takes 1/30 gallons of gas.
2nd mile takes 1/90 gallons of gas.
Total gas used is 1/30 + 1/90 = 4/90 = 2/45 gallons.

Total miles (2) / Total Gallons (2/45) = 45 miles per gallon. (The 2's cancel out)


For fun, how about you get 30mpg for the first mile and infinate mpg for the 2nd mile. Wut's the average of 30 and Infinity? Not only that, but infinite mpg is much easier to get than mph.

You got infinity mpg? Okay how about you drive for 10 years and get 10 mpg over 100,000 miles. But then you drive one mile and get infinate mpg for that mile. What's the average then?

 

no, see, Squid KNOWS...

 

As long as I'm trying to correct stuff:

 

This is a classic word problem that tests if you really understand the definition of average speed. Speed doesn't care if you accelerate fast or brake really slow during that mile around the oval, all it cares about is that you answer two questions:

1) How far did you travel?
2) How long did it take you?

Average speed doesn't care if you managed to stop and take a lunch break somewhere in the middle of your 1 mile lap. Speed doesn't care if you broke the sound barrier for 9/10 of a mile and then slammed on the brakes really hard for the last 1/10th of a mile. As long as you never travel any more or less than that 1 mile and can complete that one mile in exactly 2 minutes than you've averaged 30 mph.

 

Hmmm. I've met a lot of religious fundies who are quite sure they KNOW that theirs is the Only True Religion ™.

 

so squid wants to drive 90 on his first lap. its ok, at 90 he will almost complete his 1st lap in 40 seconds. to fit the second constraint he will have to wait at the start finish line 80 seconds in order to average 30 mph. do the average 90 for the 1st 40, 0 for the next 40 and 0 for the last 40. 90/3=30.

tell me how you plan to do the second lap......

 

The average of 30 and Infinity assuming you travel equal distance for the two mileages is 60 mpg.

As to your 2nd question the average of 10 mpg over 100,000 miles (time to travel doesn't matter) and infinite mileage over 1 mile is just ever slow slightly above 10 mpg or 10 * (1 + 1/100,000) to be exact.


The neat thing is you can achieve true infinite mpg on a Prius when you coast or use pure electric. This situation starts to describe the pulse and glide driving technique to maximize gas mileage. I've done more analysis and I'll probably repost in a more serious Prius forum as having people fret over word problems to maximize mileage is going to be more beneficial than having them fret over how to achieve a target average speed.