0951: "Working"
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 SmoothBlade
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0951: "Working"
Alt text: "And if you drive a typical car more than a mile out of your way for each penny you save on the pergallon price, it doesn't matter how worthless your time is to youthe gas to get you there and back costs more than you save."
http://xkcd.com/951/
Otherwise known as Cheesy or Machete
A conservative furry! What a rarity!
A conservative furry! What a rarity!
 Sean Quixote
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Re: 0951: "Working"
*shakes fist*
Re: 0951: "Working"
And if you drive to the gym, you're paying money to drive to a place where you pay money to ride on a pretend bicycle.

 Posts: 48
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Re: 0951: "Working"
lalalala...I'm not listening!
There's a gas station literally across the street from my neighborhood, but I will drive 5 or so miles down the road to get gas because it's cheaper. And, quite frankly, it's a much nicer looking gas station AND the one across the street is a BP (and we all know what happened there http://xkcd.com/748/).
There's a gas station literally across the street from my neighborhood, but I will drive 5 or so miles down the road to get gas because it's cheaper. And, quite frankly, it's a much nicer looking gas station AND the one across the street is a BP (and we all know what happened there http://xkcd.com/748/).
Last edited by MathUhhhSaurus on Wed Sep 14, 2011 4:19 am UTC, edited 1 time in total.
Re: 0951: "Working"
Don't forget about the inevitable wait at the other gas station as there will probably be a ridiculous line if it's 10 cents a gallon cheaper, mostly because people don't understand this.
Drives me up the freaking wall when people don't understand this.
Drives me up the freaking wall when people don't understand this.
Re: 0951: "Working"
irishnut wrote:Don't forget about the inevitable wait at the other gas station as there will probably be a ridiculous line if it's 10 cents a gallon cheaper, mostly because people don't understand this.
Drives me up the freaking wall when people don't understand this.
My favorite is when I'm in someone's car and they spend half an hour driving around and around looking for a place to park to save ten minutes walking.

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Re: 0951: "Working"
But it's the principle of the thing!! Or so they say. Sadly it took me a long time to realize this, and I do still sometimes justify it by saying "but over the course of the month I've saved about 8 dollars! That's a meal!" Also, I will continue to refuse to buy gas at the station that is ALWAYS at least 30 cents more than everything else in the area.
Re: 0951: "Working"
jpk wrote:And if you drive to the gym, you're paying money to drive to a place where you pay money to ride on a pretend bicycle.
Hopefully that's not all you're doing at the gym or else you really would be wasting your money/time. But really, assuming one is a consistent exerciser, the gym is never costefficient compared to home exercise. The only thing a gym might have over home workouts is atmosphere.
Now how much money are we all spending by being on this forum?
Re: 0951: "Working"
Well, there IS of course the exception of the second gas station being on your route anyway.
Re: 0951: "Working"
Okay, did Randall seriously write a comic just to point out the agesold concept that time=money?
I mean, it would be a little different if he pointed it out in some sort of funny or interesting way, but I'm pretty sure that everyone who has ever had to pay for their own gas has thought about this exact issue before. And the alttext as well.
This is probably one of the worst comics Randy has written in recent memory. It's not funny, original, or interesting in the slightest. I don't even understand what the point of it is. GOOMHRbait? In that case, it would be on par with "GOOMHR! I totally noticed today that the sky was blue!"
I mean, it would be a little different if he pointed it out in some sort of funny or interesting way, but I'm pretty sure that everyone who has ever had to pay for their own gas has thought about this exact issue before. And the alttext as well.
This is probably one of the worst comics Randy has written in recent memory. It's not funny, original, or interesting in the slightest. I don't even understand what the point of it is. GOOMHRbait? In that case, it would be on par with "GOOMHR! I totally noticed today that the sky was blue!"

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Re: 0951: "Working"
I like the statistical ruleofthumb for finding the cheapest gas. Once you decide to buy gas (perhaps when one quarter of your tank's capacity remains,) take note of the cheapest gas you see during the first sixth of the total distance remaining in your tank. From the second through the fifth sixths of your trip, as soon as you see gas priced at or below the cheapest price, buy it. If you haven't matched the lowest price by the time you get to the last sixth of your trip, buy gas at the next station you encounter.
Of course, this assumes a fairly even distribution of desirable and safe gas stations along the route, and that you're smart enough to fill up before your tank is dry. But it's a better strategy than nothing.
Of course, this assumes a fairly even distribution of desirable and safe gas stations along the route, and that you're smart enough to fill up before your tank is dry. But it's a better strategy than nothing.
Re: 0951: "Working"
I would have thought this would be common sense, but now it's in comic form, it's the marked end of the recession in America :america:
Hi joee!
Hi joee!
Hi joee! (origin story)
Re: 0951: "Working"
Adventures of these consumer heros helps keeping competition going and the price down for the rest of us. Even though it doesn't seem to work. Gas price is always pretty much the same on nearby stations.
And for the reference, wolframalpha converted my liters to gallons and euros to dollars and is saying I'm paying 8,37$ for a gallon of gas.
And for the reference, wolframalpha converted my liters to gallons and euros to dollars and is saying I'm paying 8,37$ for a gallon of gas.
 The Scyphozoa
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Re: 0951: "Working"
I think Randall is taking inspiration from Screechings of the Great Unwashed: stuff that doesn't deserve its own thread (or comic, whatever).
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Re: 0951: "Working"
Nyerguds wrote:Well, there IS of course the exception of the second gas station being on your route anyway.
Not really an exception since this comic addresses going out of your way for a perceived savings.
In my town, gas stations don't post their prices where they are visible from the road (something to do with local signage ordinances), so I go for the ones that are easiest to get into and out of.
If I'm out on the road, I'll start keeping track of gas prices once I'm below a quarter tank, then pull into one that's at an average price when I'm nearly empty unless there's one that's substantially cheaper before then.
Also, if there's cheaper gas five minutes "that way", why is she there?
 Djehutynakht
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Re: 0951: "Working"
KyJoCa wrote:Nyerguds wrote:Also, if there's cheaper gas five minutes "that way", why is she there?
A. Sabotage
B. She has nothing else to do, and spends all day at that gas station trying to point this out to others in a desperate attempt to feel superior, filling some sort of void. Must fight a lot with the owners.
 Awesomeness
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Re: 0951: "Working"
"Why do you work here, if your just tell customers to go to the other servo?"
Re: 0951: "Working"
I don't know what kind of gauge you have that lets you divide the last quarter of your tank into sixths accurately enough to do this...veryjaded wrote:I like the statistical ruleofthumb for finding the cheapest gas. Once you decide to buy gas (perhaps when one quarter of your tank's capacity remains,) take note of the cheapest gas you see during the first sixth of the total distance remaining in your tank. From the second through the fifth sixths of your trip, as soon as you see gas priced at or below the cheapest price, buy it. If you haven't matched the lowest price by the time you get to the last sixth of your trip, buy gas at the next station you encounter.
Of course, this assumes a fairly even distribution of desirable and safe gas stations along the route, and that you're smart enough to fill up before your tank is dry. But it's a better strategy than nothing.
Besides, none of this affects me. I put in €20 worth whatever the price, so it's the same wherever I fill up.
<ducks and runs>
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 Quicksilver
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Re: 0951: "Working"
Shut up Randall. Petrol is $5.53c a gallon over here, I'd like to save where I can.
Re: 0951: "Working"
Quicksilver wrote:Shut up Randall. Petrol is $5.53c a gallon over here, I'd like to save where I can.
I think you missed the point, boss.
Re: 0951: "Working"
I think it all depends on how far you have to drive, and how much gas you are planning on getting, the farther you drive the less likely you are to save money (I do know of one gas station that is close to two other gas stations that is typically the first to drop it's prices, and the last to raise it's prices).
gas where I live is 1.31/L (google says 4.959/gallon, and that would be canadian.). at least $0.14/L of that is tax
gas where I live is 1.31/L (google says 4.959/gallon, and that would be canadian.). at least $0.14/L of that is tax

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Re: 0951: "Working"
All of this would be solved if we chose a day every month to not buy gas!
<runs and hides with Eutychus>
<runs and hides with Eutychus>

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Re: 0951: "Working"
Quicksilver wrote:Shut up Randall. Petrol is $5.53c a gallon over here, I'd like to save where I can.
That "1 cent/mile" is accurate at $4/gallon, 40 mi/gallon, and a 10 gallon tank (assuming that "miles out of your way" includes the "there" and the "back"), which is pretty close to the conditions at which I drive. At higher prices, you actually need to save more per mile to make the trip worthwhile, since each cent saved per gallon is a smaller percentage of total cost.
I want a smartphone app that combines GPS navigation with GasBuddy's database to solve for the best gas station to fill up at, given your current location, destination, fuel economy, and tank size. Possibly with multiple results ordered based on money saved/extra time spent driving.
Re: 0951: "Working"
Yup £1.30 per litre here which equates to $8.374/us gallon. My car does 36mpg (us) so the cost per mile is 23.2 cents per mile. My tank holds 60 liters (15.85 gallons us), so for the extra two miles to be cost effective the diesel would have to be 46.4 cents cheaper, or at least 2.93 cents per gallon cheaper. That's assuming I pull into the second station on vapour, and brim the tank. Forget the time aspect, that's not important. Unless your time would otherwise be spent earning money then in a situation where driving to the other station is saving money on the total fuel cost it *is* better to make the trip.
Lost Greatest Silent Baby X Y Z. "There is no one who loves pain itself, who seeks after it and wants to have it, simply because it is pain..."

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Re: 0951: "Working"
This actually reminded me of a thought puzzle I was contemplating while on a road trip over Labor Day:
Say you're on a Road Trip. You are 300 miles from home. The gas station on the corner is selling gas at $3.00/gallon. Every mile, there is another gas station, each selling gas for an additional $0.01/gallon. So after driving 1 mile, the gas station there is selling for $3.01, and the gas station next door to your house sells gas for $6.00/gallon.
You start your journey with a full tank of gas (for easeofmath sake, 10 gallon tank). You get 30 miles/gallon, so you can make the entire trip (ending on fumes) on a single tank. However, you want to be sure that you have a full tank of gas when you leave for work in the morning, so you must refill it at the station next to your house.
What's the cheapest way to end up at home with a full tank of gas? Where should you fill up, and how often?
Does the answer change if you start with an empty tank of gas and have to decide how much to put in the tank to begin with?
Say you're on a Road Trip. You are 300 miles from home. The gas station on the corner is selling gas at $3.00/gallon. Every mile, there is another gas station, each selling gas for an additional $0.01/gallon. So after driving 1 mile, the gas station there is selling for $3.01, and the gas station next door to your house sells gas for $6.00/gallon.
You start your journey with a full tank of gas (for easeofmath sake, 10 gallon tank). You get 30 miles/gallon, so you can make the entire trip (ending on fumes) on a single tank. However, you want to be sure that you have a full tank of gas when you leave for work in the morning, so you must refill it at the station next to your house.
What's the cheapest way to end up at home with a full tank of gas? Where should you fill up, and how often?
Does the answer change if you start with an empty tank of gas and have to decide how much to put in the tank to begin with?
Re: 0951: "Working"
Brooks Hatlen wrote:All of this would be solved if we chose a day every month to not buy gas!
<runs and hides with Eutychus>
That'll be days ending in a "y" for me. Don't know what you all are doing wrong.
Re: 0951: "Working"
TheRedSeven wrote:This actually reminded me of a thought puzzle I was contemplating while on a road trip over Labor Day:
Say you're on a Road Trip. You are 300 miles from home. The gas station on the corner is selling gas at $3.00/gallon. Every mile, there is another gas station, each selling gas for an additional $0.01/gallon. So after driving 1 mile, the gas station there is selling for $3.01, and the gas station next door to your house sells gas for $6.00/gallon.
You start your journey with a full tank of gas (for easeofmath sake, 10 gallon tank). You get 30 miles/gallon, so you can make the entire trip (ending on fumes) on a single tank. However, you want to be sure that you have a full tank of gas when you leave for work in the morning, so you must refill it at the station next to your house.
What's the cheapest way to end up at home with a full tank of gas? Where should you fill up, and how often?
Does the answer change if you start with an empty tank of gas and have to decide how much to put in the tank to begin with?
The answer to the last question, I think, is pretty obvious: since the cheapest gas available is at the first station, filling up there is just step 0 of the algorithm. I see no way that a partial fillup and topping off at the more expensive stations improves your situation. So no, the rest of the answer doesn't change, just the total number of gallons you put in the tank in the course of the puzzle.
I'm tempted to say that the answer to the puzzle as stated is the obviously wrong one: fill up at each mile mark. That way you're always putting the cheapest gas into your tank. Since your puzzle doesn't take the expense of stopping (time and aggravation and the "wtf" look from the gas station attendant) none of those are factors, so your puzzle's answer isn't very applicable in the real world.
I'd be curious to know if there's a better answer from a better mathematician, though.

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Re: 0951: "Working"
TheRedSeven wrote:This actually reminded me of a thought puzzle I was contemplating while on a road trip over Labor Day:
Say you're on a Road Trip. You are 300 miles from home. The gas station on the corner is selling gas at $3.00/gallon. Every mile, there is another gas station, each selling gas for an additional $0.01/gallon. So after driving 1 mile, the gas station there is selling for $3.01, and the gas station next door to your house sells gas for $6.00/gallon.
You start your journey with a full tank of gas (for easeofmath sake, 10 gallon tank). You get 30 miles/gallon, so you can make the entire trip (ending on fumes) on a single tank. However, you want to be sure that you have a full tank of gas when you leave for work in the morning, so you must refill it at the station next to your house.
What's the cheapest way to end up at home with a full tank of gas? Where should you fill up, and how often?
Does the answer change if you start with an empty tank of gas and have to decide how much to put in the tank to begin with?
Perhaps I'm misunderstanding, but it seems obvious that you should get as much gas as possible at each gas station you pass (i.e. full tank at the cheapest, then just enough to fill all the way at the secondcheapest, etc.): since the length of the trip is constant, and you need to end with a full tank of gas, the total amount of gas you get is the same. And so any amount you don't get from a cheaper gas station you'll have to pay more for eventually anyway.

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Re: 0951: "Working"
jpk wrote:TheRedSeven wrote:This actually reminded me of a thought puzzle I was contemplating while on a road trip over Labor Day:
Say you're on a Road Trip. You are 300 miles from home. The gas station on the corner is selling gas at $3.00/gallon. Every mile, there is another gas station, each selling gas for an additional $0.01/gallon. So after driving 1 mile, the gas station there is selling for $3.01, and the gas station next door to your house sells gas for $6.00/gallon.
You start your journey with a full tank of gas (for easeofmath sake, 10 gallon tank). You get 30 miles/gallon, so you can make the entire trip (ending on fumes) on a single tank. However, you want to be sure that you have a full tank of gas when you leave for work in the morning, so you must refill it at the station next to your house.
What's the cheapest way to end up at home with a full tank of gas? Where should you fill up, and how often?
Does the answer change if you start with an empty tank of gas and have to decide how much to put in the tank to begin with?
The answer to the last question, I think, is pretty obvious: since the cheapest gas available is at the first station, filling up there is just step 0 of the algorithm. I see no way that a partial fillup and topping off at the more expensive stations improves your situation. So no, the rest of the answer doesn't change, just the total number of gallons you put in the tank in the course of the puzzle.
I'm tempted to say that the answer to the puzzle as stated is the obviously wrong one: fill up at each mile mark. That way you're always putting the cheapest gas into your tank. Since your puzzle doesn't take the expense of stopping (time and aggravation and the "wtf" look from the gas station attendant) none of those are factors, so your puzzle's answer isn't very applicable in the real world.
I'd be curious to know if there's a better answer from a better mathematician, though.
10 gallons * $6.00/gallon = $60.00.
The cost of topping off at each station is [math]\sum_{i=1}^{300} (3+0.01i)/30[/math] = $45.05. (The "/30" is for 1 thirtieth of a gallon per topoff.)
Running it for topping off every other station yields [math]\sum_{i=1}^{150} (3+0.02i)/15[/math] = $45.10, so I'm pretty sure topping off every mile is the optimal solution to the problem as stated  ignoring the effect of stopping on fuel economy, aggravation, etc.
Last edited by keiranhalcyon31 on Wed Sep 14, 2011 6:35 am UTC, edited 4 times in total.
Re: 0951: "Working"
Ah, but what if the fact that he has no customers convinces the guy running the station that he needs to lower his prices?
Then you will be saving money every time you buy gas from him for the rest of your life.
Then you will be saving money every time you buy gas from him for the rest of your life.
Re: 0951: "Working"
Agreed. The cheapest solution is to fill up at every opportunity.
Lost Greatest Silent Baby X Y Z. "There is no one who loves pain itself, who seeks after it and wants to have it, simply because it is pain..."
Re: 0951: "Working"
Re minimum wage: this is why I only do comparison eshopping from work .
Re: 0951: "Working"
I regularly go out of my way to get petrol. The typical difference between a motorway price and a good/low price is approx 47 cents ($9 compared to $8.53). I typically put 15 gallons into my car. That gives me a saving of over $7 for a typical 3 mile diversion, which costs me around 90c and five minutes to drive. So, with conservative rounding, I make $6 in five minutes, or $72/hour.
Since that saving is posttax, I would need to earn around $110/hour to make the same money working.
Since that saving is posttax, I would need to earn around $110/hour to make the same money working.
Re: 0951: "Working"
At the current rate (which is quite good lately) I'm paying $8.67 per gallon in my private car. In my leased car, which had it's gas price fixed for a four year period in the peak oil times of july 2008, I pay $8.93 per gallon. That's right, $8.93. It's probably cheaper for me to cross the pond and fill up my car over there every time.
Hooray for Dutch taxes! \o/
Hooray for Dutch taxes! \o/
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 Eternal Density
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Re: 0951: "Working"
This is why I pretty much always buy petrol at the same place, cos it's only a few seconds off the freeway that I take twice a day.
Also, wow, an xkcd that is meaningful and potentially helpful!
Also, wow, an xkcd that is meaningful and potentially helpful!
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In the Marvel vs. DC filmmaking war, we're all winners.
Re: 0951: "Working"
Red Hal wrote:Yup £1.30 per litre here which equates to $8.374/us gallon. My car does 36mpg (us) so the cost per mile is 23.2 cents per mile. My tank holds 60 liters (15.85 gallons us), so for the extra two miles to be cost effective the diesel would have to be 46.4 cents cheaper, or at least 2.93 cents per gallon cheaper.
A 60 liter tank huh? My car has only a 40 liter tank, but it's a smallsized vehicle of the "how small can we make it and still cram four sixfoottall men into it?" variety.
Re: 0951: "Working"
keiranhalcyon31 wrote:snip
10 gallons * $6.00/gallon = $60.00.
The cost of topping off at each station is [math]\sum_{i=1}^{300} (3+0.01i)/30[/math] = $45.05. (The "/30" is for 1 thirtieth of a gallon per topoff.)
Running it for topping off every other station yields [math]\sum_{i=1}^{150} (3+0.02i)/15[/math] = $45.10, so I'm pretty sure topping off every mile is the optimal solution to the problem as stated  ignoring the effect of stopping on fuel economy, aggravation, etc.
To play with this some more, lets take the continuum limit of the gas stations and assume you top up continuously. At distance x, the price is P(x) = 3 + x / 100. For each infinitesimal distance dx we travel, we need dx/(30 mpg) gallons of gas, costing P(x)dx/30. The total cost is
[math]\int_0^{300}\left(3 + \frac{x}{100}\right) \frac{dx}{30} = 45[/math]
which is slightly less than filling up every mile. In fact, filling up in larger increments is the mathematical analogue to taking a Riemann sum. In this case, the cost function is strictly increasing, and we take a right Riemann sum, so the Riemann sum overestimates the integral. Thus, if we always top up, we spend the least when we do so as frequently as possible.
To model leaving some empty space in the tank, introduce a filling rate function f(x) and require [imath]\int_0^{300}f(x)\,dx=10[/imath]. The total cost is then [imath]\int_0^{300}P(x)f(x)\, dx[/imath].
Of course, filling up continuously makes no sense. Yay for useless mathematical abstractions!
Re: 0951: "Working"
I've learned this the hard way with my electronics projects. "Oh, look, this store in Hong Kong offers free shipping and I can get x, y, z cheaper than from San Fransisco, but I still need a, b, and c so I'll place two orders. 2 days later, the package from San Fransisco has arrived, but I'm missing 'y' so I can't start. Two weeks later, x, y, and z arrive. Then there is a whole other layer since I got y and z simply to save a few pennies on 'k' that would have worked instead. I just have to assemble y and z into a k, which will take several hours of my time researching and debugging.
On the bright side, in my short 'adulthood' (the 2.6 years since I turned 18), I managed to learn at least one thing, being cheap simply passes the cost from one set off assets (money) to another (time). That's a concept that I wish didn't take so long to learn, if only I had thought of paying someone to tell me that.
On the bright side, in my short 'adulthood' (the 2.6 years since I turned 18), I managed to learn at least one thing, being cheap simply passes the cost from one set off assets (money) to another (time). That's a concept that I wish didn't take so long to learn, if only I had thought of paying someone to tell me that.
Re: 0951: "Working"
lemmings wrote:I've learned this the hard way with my electronics projects. "Oh, look, this store in Hong Kong offers free shipping and I can get x, y, z cheaper than from San Fransisco, but I still need a, b, and c so I'll place two orders. 2 days later, the package from San Fransisco has arrived, but I'm missing 'y' so I can't start. Two weeks later, x, y, and z arrive. Then there is a whole other layer since I got y and z simply to save a few pennies on 'k' that would have worked instead. I just have to assemble y and z into a k, which will take several hours of my time researching and debugging.
On the bright side, in my short 'adulthood' (the 2.6 years since I turned 18), I managed to learn at least one thing, being cheap simply passes the cost from one set off assets (money) to another (time). That's a concept that I wish didn't take so long to learn, if only I had thought of paying someone to tell me that.
YES! As an amateur electronics enthusiast myself I could not agree more.
Also, I have been calculating the cost of things using minimum wage as a guide for a long time now. I think it's an excellent way to organise one's thoughts on the cost of time.
Re: 0951: "Working"
For the love of God
http://theoatmeal.com/comics/senior_year
*shakes fist* I hoped that at least here I would have been spared the gallons/miles crap ):
The funniest fact is that some of you make all the calc with gallons, but when it comes to measuring the tank capacity, they go with litres. MADNESS!!!
Metric vs imperial flame war ensues...
And, huh, here in Italy gas is 2.1806 dollars per liter, which converts to 8.253571 dollars per gallon, so I guess from what I read here that here in Europe we are pretty much screwed. We can more or less cross an entire city to get cheaper gas... ):
http://theoatmeal.com/comics/senior_year
*shakes fist* I hoped that at least here I would have been spared the gallons/miles crap ):
The funniest fact is that some of you make all the calc with gallons, but when it comes to measuring the tank capacity, they go with litres. MADNESS!!!
Metric vs imperial flame war ensues...
And, huh, here in Italy gas is 2.1806 dollars per liter, which converts to 8.253571 dollars per gallon, so I guess from what I read here that here in Europe we are pretty much screwed. We can more or less cross an entire city to get cheaper gas... ):
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