OK, now that someone seems to have solved that one (and I’m too lazy to check it), I’ve got another hard math problem for you:
Prove that all non-trivial zeros of the Riemann zeta function have 1/2 as their real part.
I approached this problem (the OP) the way one does conversions, (ie. cancel the units.) We get $2/gallon (constant), 18 miles per gallon originally, and 18.0000396 mi/gal when the car has the nickel in it (this is based on the assumtion that the miles/gallon ratio decreases linearly [slope = -1] with the mass of the car.) Converting the grams of the nickel to pounds, assuming there’s 2.2 kg/pound yields a .0011 lb nickel.
Having established, invert the miles per gallon to gallons per miles.
So the car originally gets (1/18 gal/mile) * (2/gal) * (x miles) = .05
x = .45000… (27 zeros, if I counted correctly) miles.
So the car originally uses a nickel’s worth of gas almost exactly every .45 miles.
The car, once it’s got a nickel in it:
(1/18.0000396 gal/mile)*(2/gal)*(x miles) = .05.
Here x = .450004500045000… miles
So when the car gains .0011 (a nickel’s weight) pounds it burns a nickel .0000045 miles before the original car.
Seems reasonable to me, but I haven’t checked it.
Doh… should have checked. My answer can’t be right because somehow my math had the car gaining efficiency (miles/gallon) with additional weight. I think the general approach is right though. :smack:
Another way to think of this is that it always pays to pick up a nickel.
As a product of the great depression I have a keen appreciation of the value of money. In fact there are those among my friends who say that I over-appreciate money. I head one say to another, “That Simmons is tighter than the skin on a grape” just the other day.
I always pick up coins I see laying on the walkway, even pennies. I do it even though it will cost me a little extra in food to get the energy to carry the extra weight.
I just can’t help it.
Gee Blaneg2 started this whole brouhaha and hasn’t been seen since post #4. Why do some “Dopers” do that ?
Not a doper–guest.
Even though bending over to pick up the nickel has been mentioned, I don’t think the weight loss involved in doing so has been factored in. Yet.
In order to exhale 5 grams of carbon, you’d only have to expel 10 liters of carbon dioxide. The engine doesn’t even have to be running, as lektrikpuke suggested–you just have to take time for a few extra breaths. And the sweating…
And also, everyone’s forgetting that the longer you drive, the less your car weighs due to tire wear, the wind eroding off small pieces of your car (Ok… so maybe that’s negligible), but also the fact that you use gas. Gas also has a weight… and would probably matter more than that nickel.
His homework was completed. 
Why stick around?
LOL Astro
And probably true.
[Grumpy Old Man]
A “thank you” would have been nice but you know these kids today. Back in my day day we respected our elders…
[/Grumpy Old Man]
As a theoretical problem you should do your own homework and not depend on others.
As a practical problem there are far to many factors and considerations to arrive at a solution and as such it doesn’t make a “Nickels Worth of Difference!”
I thought I was being so very clever…
I see now I just whitewashed Mr. Sawyer’s fence.
harrumph!
Igloo
and I was so anxious to help !!!
:smack:
I am so glad they brought back the “smack the head” smilie.