Plane question fun? Try this one.

[Sean 94z28]

You drive your F-body 30MPH through town for 1 mile. You're late for an appoinment and you are going a total of 2 miles from your start to your destination. Now that you have 1 mile of open road to go (assume no speed limit), how fast will you need to go to average:

51 MPH (you'll be just on time)?
or
60 MPH (time to spare)?

[zebragirl83]

If I understand the question right....
51mph= 72mph
and
60mph= 90 mph


right? maybe I'm an idiot?

I'm a dork regardless... why are we doing math problems... we are hurtin' for somethin' to talk about!!!

[Sean 94z28]

right? maybe I'm an idiot?

Well that would make me an idiot also. I did the same thing.

In fact, just like me, I would say your not an idiot for recognizing that your answer is too simple to be right.

HINT - even Fred's machine does not have the HP to get you there on time

[TruckMuddr]

allright, you lost me on that one. don't you need to time in there somewhere. I mean 30MPH for 1 mile will take you 2 mins. I'm lost on the rest.

[fastTa]

Not enough information to calculate a finite conclusion. Maybe if you include a required time parameter.

[Sean 94z28]

You can calculate the time parameter for both speeds right?

51 MPH for 2 miles
60 MPH for 2 miles (easy one)

Truck did half the math and stopped. And for one of the 2 ave speeds you might call this a trick question. But it definately has an answer and a logical explanation why that is the answer.

[TruckMuddr]

I don't see how you can say 51 or 60 mph for 2 miles when you allready did 1 of the 2 miles at 30mph and your first post said total for 2 miles.

but just doin the conversion.

30 mile/hour = 0.5 mile/minute x 2 miles = 4 minutes.
60 mile/hour = 1 mile/minute x 2 miles = 2 minutes.
51 mile/hour = 0.85 mile/minute x 2 miles =2.35 minutes.


I still say the first post is worded wrong.

[fastTa]

You've already answered your own question :

Now that you have 1 mile of open road to go (assume no speed limit), how fast will you need to go to average:

51 MPH (you'll be just on time)?
or
60 MPH (time to spare)?

Your question specifically asks what speed is required to end up with a certain average. Well...if you travel at a relatively consistent speed of 51 MPH within the last mile, then your average will be 51 MPH within the last mile. If you travel at a relatively consistent speed of 60 MPH within the last mile, then your average will be 60 MPH within the last mile.

I think I know what you are getting at, but you asked the question inappropriately and that's why it is confusing.

[fastTa]

If I understand the question right....
51mph= 72mph
and
60mph= 90 mph


right? maybe I'm an idiot?

I'm a dork regardless... why are we doing math problems... we are hurtin' for somethin' to talk about!!!

You are mathematically correct according to how the question is worded.

[Sean 94z28]

You've already answered your own question :



Your question specifically asks what speed is required to end up with a certain average. Well...if you travel at a relatively consistent speed of 51 MPH within the last mile, then your average will be 51 MPH within the last mile. If you travel at a relatively consistent speed of 60 MPH within the last mile, then your average will be 60 MPH within the last mile.

I think I know what you are getting at, but you asked the question inappropriately and that's why it is confusing.

I didn't say it specifically (and now I wished I had ), but the question asks how to average those speeds over the full distance, not just the last or first miles. I really don't think it is that confusing though "Now that you have 1 mile of open road to go (assume no speed limit), how fast will you need to go to average......."


Well, you pretty much answered the question for 60MPH. Truck is exactly right. If you need to average 2 miles in 2 minutes, and you already spent 2 minutes on the first mile. than the answer is - you can't do it. And that is the explanation why. Now that you know this, it should be easy to calculate and answer for 51.

It is an exercise to show that you can't simply use the formula for average on numbers that are ratios.

[Sean 94z28]

You are mathematically correct according to how the question is worded.

No. I asked that ratios be averaged, and not simple whole numbers. That is not mathmatically correct.

She correctly answered the average of 30 and 51, and 30 and 60, respectively. She did not answer how to average 51 and 60 MPH for 2 miles after you have already travelled one mile at 30 MPH.

It may have been worded less than perfectly, but it most certainly wasn'yt worded in a way that would make those answers correct.

Maybe I should have said how fast the wheels were moving.

[Jay 02 TA ws6]

You drive your F-body 30MPH through town for 1 mile. You're late for an appoinment and you are going a total of 2 miles from your start to your destination. Now that you have 1 mile of open road to go (assume no speed limit), how fast will you need to go to average:

51 MPH (you'll be just on time)?
or
60 MPH (time to spare)?

(30 miles)/(1 hour) = (1 mile)/(x hours)
30x = 1
x = 1/30 hours... .0333333333333333333 hours

(1 hour)/(60 minutes) = (.0333333333333333 hours)/(x minutes)

(x)/60 = .03333333333333333333333
x = 60 * .033333333333333333333
x = 2

So you traveled 20 mph for 2 minutes, and went 1 mile.

You need to average 51 mph to make it there on time and so far your average is 20.

Your total distance to travel is 2 miles, and you need to travel 51 mph during that time to make it on time.

(51 miles)/(1 hour) = (2 miles)/(x hours)
51x = 2
x = 2/51
x = .039215686 hours

(1 hour)/(60 minutes) = (.039215686 hours)/(x minutes)
x/60 = .039215686
x = 2.35294 minutes

Your trip at 51 mph can only take a total of 2.35294 minutes. Since you've already taken 2 minutes poking along at 30 mph, you only have 0.35294 minutes and you have 1 mile to go.

(60 minutes)/(1 hour) = (.35294 minutes)/(x hours)
60x = .35294
x = .005882359 hours

(1 mile)/(.005882359 hours) = (x miles)/(1 hour)
1/.005882359 = x
x = 169.99 miles.

You need to average 169.99 mph for the next mile in order to make it on time.

Take in to account that much of this time will be spent accelerating from 30 to 169.99 mph, and I would think you should finish this trip well in excess of 200 mph. To breakdown the acceleration, that involves derivatives and exponentials, and I'm not going to do that here.

To figure out the 60 mph, just plug in 60 where you see 51... I would do it, but I am tired.

[TruckMuddr]

(30 miles)/(1 hour) = (1 mile)/(x hours)
30x = 1
x = 1/30 hours... .0333333333333333333 hours

(1 hour)/(60 minutes) = (.0333333333333333 hours)/(x minutes)

(x)/60 = .03333333333333333333333
x = 60 * .033333333333333333333
x = 2

So you traveled 20 mph for 2 minutes, and went 1 mile.

You need to average 51 mph to make it there on time and so far your average is 20.

Don't you mean "you traveled 30 mph for 2 minutes, and went 1 mile."

[Jay 02 TA ws6]

Don't you mean "you traveled 30 mph for 2 minutes, and went 1 mile."

Yes, yes I do.

[Sean 94z28]

Nice Jay,

60 is the easy one because you would have to go 2 miles in 2 minutes. You already used up the 2 minutes going the first mile at 30. So, you can't do it.

I use this one trips with friends to illustrate how time spend at lower speeds, is very difficult to make up, even over a longer distance.

You are correct on 51. You have about 1/3 of a minute to cover the second mile if you could acheive that speed instantly. And the actual answer would depend on how fast you can accelerate to there.