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Fun calculus problem for ZR1

 
Old 05-28-2019, 11:00 AM
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SouthernSon
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Default Fun calculus problem for ZR1

Problem: Imagine an east to west coast 'autobahn' highway with no speed limits. If one were to figure a fuel stop takes 10 minutes on average where would speed and fuel mileage give one the quickest arrival at the other end?
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Old 05-28-2019, 11:39 AM
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Rinaldo Catria
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What are the cars mpg stats at various speeds? That info information is needed, no?
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Old 05-28-2019, 11:52 AM
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Thomasmoto
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This came up in a group I was in last spring. It's almost impossible to calculate with so many variables, but IIRC it was around 33-34 hours time, but no idea on fuel used. As far as sources go I'll have to plead the 5th.
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Old 05-28-2019, 07:41 PM
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True that we don't have any quantitative figures to ascertain the correct amount but the formula depicting the relationship of the variables can be shown.
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Old 05-28-2019, 10:07 PM
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3000 miles divided by 100 mph avg speed equals 30 hours...simple enough...

3000 miles divided by 15 mpg in overdrive 7th or 8th gear equals 200 gals ...again...simple enough
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Old 05-29-2019, 10:38 AM
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Okay, math geniuses, I know someone has a handle on this equation. It reminds me of the problem of a farmer with so much of this fence that costs this and so much of another type material that costs this and wants to get so much road frontage and yet retain so much acreage while minimizing costs...etc.. (IIRC). Someone remembers calculus, right?? It was decades ago for me.
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Old 05-30-2019, 07:12 AM
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This is algebra though not calculus.
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Old 05-30-2019, 08:55 AM
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Originally Posted by UnhandledException View Post
This is algebra though not calculus.
With the number of variables I would think calculus may be more appropriate although the two can be inseparable. One needs knowledge of algebra to work with calculus.

https://www.quora.com/How-is-calculu...t-from-algebra
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Old 05-30-2019, 08:56 AM
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Originally Posted by SouthernSon View Post
With the number of variables I would think calculus may be more appropriate although the two can be inseparable. One needs knowledge of algebra to work with calculus.

https://www.quora.com/How-is-calculu...t-from-algebra
I am just pulling your leg
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Old 05-30-2019, 10:33 AM
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Originally Posted by SouthernSon View Post
With the number of variables I would think calculus may be more appropriate although the two can be inseparable. One needs knowledge of algebra to work with calculus.

https://www.quora.com/How-is-calculu...t-from-algebra
What he said.

Any info on mpg at various (steady) speeds? We can see road racing mpg's are pretty bad. We need to add time spent with the troopers during "safety" stops into the equation.
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Old 05-30-2019, 12:33 PM
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https://images.app.goo.gl/ntXfvz14MXG28ZF16 I have someone working on it.
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Old 05-30-2019, 02:31 PM
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Originally Posted by Rinaldo Catria View Post
https://images.app.goo.gl/ntXfvz14MXG28ZF16 I have someone working on it.
I could have done so much better in college had I had one of those!
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Old 05-30-2019, 11:35 PM
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assuming:
25 at 60
20 at 75
15 at 90

which one is best?
18 gallon tank

25*18 = 450 / 2800 = 6.2 stops or 7 stops = 70 min downtime
20*18 = 360 / 2800 = 7.7 stops or 8 stops = 80 min downtime
15*18 = 270 / 2800 = 10.3 stops or 11 stops = 1100 min downtime

2800 miles
60 mph = 46.66 hrs + 70 min down = 47.82 hrs
75 mph = 37.33 hrs + 80 min down = 38.66 hrs
90 mph = 31.11 hrs + 1100 min down = 49.44 hrs

so I think it's going to be in the 80 mph range, more calculations would get you closer of course.
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Old 05-30-2019, 11:41 PM
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Originally Posted by Higgs Boson View Post
assuming:
25 at 60
20 at 75
15 at 90

which one is best?
18 gallon tank

25*18 = 450 / 2800 = 6.2 stops or 7 stops = 70 min downtime
20*18 = 360 / 2800 = 7.7 stops or 8 stops = 80 min downtime
15*18 = 270 / 2800 = 10.3 stops or 11 stops = 1100 min downtime

2800 miles
60 mph = 46.66 hrs + 70 min down = 47.82 hrs
75 mph = 37.33 hrs + 80 min down = 38.66 hrs
90 mph = 31.11 hrs + 1100 min down = 49.44 hrs

so I think it's going to be in the 80 mph range, more calculations would get you closer of course.
Drop that extra zero from the 90 mph calculations and you will get a better picture.
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Old 05-31-2019, 07:22 AM
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Higgs Boson
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Originally Posted by range96 View Post
Drop that extra zero from the 90 mph calculations and you will get a better picture.
lol. yes that's true. math after bedtime never works.

so 90 is 32.94 hrs, so something faster would be the answer.

however this is all based on the assumption that we know the mpg:mph ratios already.
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Old 05-31-2019, 11:14 AM
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Originally Posted by Higgs Boson View Post
assuming:
25 at 60
20 at 75
15 at 90

which one is best?
18 gallon tank

25*18 = 450 / 2800 = 6.2 stops or 7 stops = 70 min downtime
20*18 = 360 / 2800 = 7.7 stops or 8 stops = 80 min downtime
15*18 = 270 / 2800 = 10.3 stops or 11 stops = 1100 min downtime

2800 miles
60 mph = 46.66 hrs + 70 min down = 47.82 hrs
75 mph = 37.33 hrs + 80 min down = 38.66 hrs
90 mph = 31.11 hrs + 1100 min down = 49.44 hrs

so I think it's going to be in the 80 mph range, more calculations would get you closer of course.
I don't think those linear calculations address the sought intersection of all the variables first mentioned in the problem.
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Old 05-31-2019, 01:41 PM
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Originally Posted by SouthernSon View Post
I don't think those linear calculations address the sought intersection of all the variables first mentioned in the problem.
what variables? the question is 100% linear as posed.
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Old 05-31-2019, 02:06 PM
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Originally Posted by SouthernSon View Post
I don't think those linear calculations address the sought intersection of all the variables first mentioned in the problem.
I think that simplified method is close enough. Without exact mpg for different speeds is futile. If mpg could be provided as a function of speed a more accurate estimate (or even an exact answer) could be provided. Then again, how do you estimate time spent with the trooper when he pulls you over 100?
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Old 05-31-2019, 09:19 PM
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SouthernSon
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Originally Posted by range96 View Post
I think that simplified method is close enough. Without exact mpg for different speeds is futile. If mpg could be provided as a function of speed a more accurate estimate (or even an exact answer) could be provided. Then again, how do you estimate time spent with the trooper when he pulls you over 100?
Well, there is always that. We have the variable of number of 10 minute stops which vary with mpg which depends upon speed while speed determines total time which gets back to mph and number of 10 minute fuel stops. All of these variables are dependent upon each other and dynamic. I would think a calculus equation would address this problem very well. I really don't see anything linear. I suppose one could keep calculating equations with different values and might be able to come up to a somewhat ballpark figure but nothing more. I believe this problem would be a good exercise for someone well versed in calculus.
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Old 05-31-2019, 09:26 PM
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Originally Posted by SouthernSon View Post
Well, there is always that. We have the variable of number of 10 minute stops which vary with mpg which depends upon speed while speed determines total time which gets back to mph and number of 10 minute fuel stops. All of these variables are dependent upon each other and dynamic. I would think a calculus equation would address this problem very well. I really don't see anything linear. I suppose one could keep calculating equations with different values and might be able to come up to a somewhat ballpark figure but nothing more. I believe this problem would be a good exercise for someone well versed in calculus.
i think you're overcomplicating it.
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