Fun calculus problem for ZR1
05-28-2019, 11:00 AM
#1
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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? 
05-28-2019, 11:52 AM
#3
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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.
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.
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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05-30-2019, 08:55 AM
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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
https://www.quora.com/How-is-calculu...t-from-algebra
05-30-2019, 08:56 AM
#9
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
https://www.quora.com/How-is-calculu...t-from-algebra
05-30-2019, 10:33 AM
#10
Le Mans Master
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
https://www.quora.com/How-is-calculu...t-from-algebra
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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05-30-2019, 02:31 PM
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https://images.app.goo.gl/ntXfvz14MXG28ZF16 I have someone working on it.
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.
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.
05-30-2019, 11:41 PM
#14
Le Mans Master
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.
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.
05-31-2019, 07:22 AM
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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.
05-31-2019, 11:14 AM
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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.
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.
05-31-2019, 01:41 PM
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05-31-2019, 02:06 PM
#18
Le Mans Master
05-31-2019, 09:19 PM
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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?
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.
05-31-2019, 09:26 PM
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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.
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.