10/12/15
Section A
Queens
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The Gas Station Problem every driver recognizes the fluctuations in gas prices that happen almost on a
weeky basis. In many areas, local radio stations have special reports on the location of the gas station
with the lowest prices per gallon for regular gas. Of course that station is likely to be across town form
where you’re driving. But, is it worth the drive across town for less expensive gas? If you know the
locations and the prices at all gas stations, at which station should you buy your gas?
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The first base case where the seconds station’s rate is five cents less than the original gas station’s
rate. The second is that case where the gas station is 10 cents less at the next station, and the last is
20 cents less at the next station. We are assuming the mpg of the car is 25 mpg, the cost of gas at the
original station is $2.30, and the tank can carry 16 gallons of gas and is currently 1/4 full.
Miles Away vs. Cost Difference
Cost Difference
4
5 cents
2
10 cents
5
10
15
20
Miles Away
20 cents
-2
-4
*Note that the Cost difference from 0 miles is 0 for all three distances*
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The car has an average of 25 mpg.
The car has a 16 gallon tank.
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Section A
Queens
Currently the tank is a quarter full (4 gallons) which mean you have to fill up 12 gallons.
The cost of the gas in the tank currently is $2.30.
The car is currently at a gas station with a price of $2.30.
We assumed the gas stations were 5 miles away, 10 miles away, and 15 miles away and that
that was the only distance extra traveld from the route.
We assumed $0.05 less, $0.10 less, and $0.20 less at each of these distances to figure our
how far out it was worth it for how much less.
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You burn 1/5 of a gallon to go 5 miles out of the way.
Therefore you will burn 2/5 of a gallon to go 10 miles away, 3/5 for 15 miles, 4/5 for 20 miles, etc.
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If you are burning this gas to get tp the cheaper gas station the cost of gas burned is accounted for.
Cost to go out of the way 5 miles= $0.46.
Therefore 10 miles = $0.92
Therefore 15 miles = $1.38
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If you were to fill up at the gas station where you are now it would cost $27.60.
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It costs an extra $0.31 to go five miles away for $0.05 less cost for a gallon of gas.
It costs an extra $1.22 to go ten miles away for $0.05 less cost for a gallon of gas.
It costs an extra $2.13 to go fifteen miles away for $0.05 less cost for a gallon of gas.
It costs an extra $3.04 to go twenty miles away for $0.05 less cost for a gallon of gas.
It costs an extra $3.95 to go twenty miles away for $0.05 less cost for a gallon of gas.
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Section A
Queens
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You save $0.30 to go five miles away for $0.10 less cost for a gallon of gas.
It costs an extra $0.60 to go ten miles away for $0.10 less cost for a gallon of gas.
It costs an extra $1.50 to go fifteen miles away for $0.10 less cost for a gallon of gas.
It costs an extra $2.40 to go twenty miles away for $0.10 less cost for a gallon of gas.
It costs an extra $3.30 to go twenty miles away for $0.10 less cost for a gallon of gas.
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d = distance to travel to gas station
p = miles per gallon
h = cost of gas currently in car
g = tank capacity
t = gallons currently in tank
c = cost at current gas station
m = difference in cost
Gas Problem
5 cents, 10 cents, and 20 cents less at the next station
The first base case where the seconds station’s rate is five cents less than the original gas station’s
rate. The second is that case where the gas station is 10 cents less at the next station, and the last is
20 cents less at the next station. We are assuming the mpg of the car is 25 mpg, the cost of gas at the
original station is $2.30, and the tank can carry 16 gallons of gas and is currently 1/4 full.
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For this problem we figured out whether or not it would be worth it to drive across town for
cheaper gas. The cheaper option would vary based on the difference in price per gallon and the distance that needed to be travelled to the cheaper gas. When determining what option was cheaper you
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Section A
Queens
were already located next to one gas station with a price of $2.30 per gallon. $2.30 per gallon was the
national average at the time this problem was solved as determined by AAA. The price of gas at the
station across town was either 5, 10, or 20 cents less per gallon. The problem was solved for stations 5,
10, 15, 20, and 25 miles away from the current position. We decided it would be worth it to drive to a
cheaper gas as long as money was saved. Therefore it would not be worth it to drive any distance, five
miles or greater, for gas that is 5 cents cheaper. If gas was 10 cents cheaper per gallon it would be
worth it to drive out 5 miles for gas, but not much farther. And for 20 cent cheaper gas it is worth it to
drive out fifteen miles to get gas.
After solving that we made an equation that has any variable necessary for determining whether
or not someone would save money driving to a cheaper gas station. The driver would have to know
their car’s average mpg and how many gallons their tank can hold. Also the driver would have to know
the distance away the gas station is, how much cheaper the gas is, and the cost of the gas currently in
the car. The equation would calculate the cost to fill up the tank at this gas station, and as long as the
driver can calculate how much it will cost them to fill up at the current gas station they can determine
which station would be cheaper to go to.
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The next step in solving this problem would be to have more strenuous circumstances. This
would include if there was fluctuating gas prices determined by the days of the week and therefore if
someone should fill their tank up partially or fully. We also would have tried a scenario where the gas
station was out of the way of the route of a person, and therefore that had to travel to the gas station
and back. We also were looking into the cost difference for high-octane gas and seeing if those price
differences, and the increased efficiency of the car would make it more/ less cost effective to travel to a
certain gas station. We also would consider the time it would take to travel to another gas station and if
it would be worth it to travel out of the way.
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We divided and conquered and aggred on an initial method after brainstorming possible methods. We
then created an equation to generalize our solution so it can be applicable for more than our assumptions. We learned how to attack problem effecively, to first start with a simple data and build on it, and
how to save money at a gas station. Also, we learned that it was easier to make a lot of assumptions to
simplify and problem and then find a larger equation that could account for varying circumstances.
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