Fuel efficiency in the U.S. is measured in miles per gallon. The higher the miles per gallon, the less money a person will have to spend on a car trip.
If you ever make a calculation involving miles per gallon, keep track of the units! The units of miles per gallon is \(\frac{\text{miles}}{\text{gallon}}\).
Note that \(20\) miles per gallon is the same statement as one gallon per \(20\) miles. That means \(\frac{20 \text{ miles}}{1 \text{ gallon}} = \frac{1 \text{ gallon}}{20 \text{ miles}}\)
1.
A person is going to take a \(200\) mile trip. Their vehicle is said to
get 18 miles per gallon. How many gallons should they expect to use for
the trip?
The ending units we want is "gallons", so we want gallons to be in the numerator (top) of the fraction. We can multiply the \(200\) miles by \(\frac{1 \text{ gallon}}{18 \text{ miles}}\)
\[200 \text{ miles} \cdot \frac{1 \text{ gallon}}{18 \text{ miles}}\]
The "miles" units cross cancel to leave us with gallons, like we wanted.
\[200 \cancel{\text{ miles}} \cdot \frac{1 \text{ gallon}}{18 \cancel{\text{ miles}}}\]
\[\frac{200 \text{ gallons}}{18} \approx 11.11 \text{ gallons}\]
2.
A car gets 24 miles per gallon. A person did not have their phone
GPS turned on and they want to know how far they have traveled. When
they gas up, they realized they spent 12 gallons of gas. How far have
they traveled?
The ending units we want are "miles" (distance traveled), so we will make sure to have miles in the numerator (top) of the fraction. We can write 24 miles per gallon as \(\frac{24 \text{ miles}}{\text{gallon}}\) as it has miles in the numerator. We could also write it as \(\frac{\text{gallon}}{24 \text{ miles}}\), but miles would be in the denominator.
Multiply the \(\frac{24 \text{ miles}}{\text{gallon}}\) by \(12\) gallons to make the "gallons" units cross cancel.
\[\frac{24 \text{ miles}}{\text{gallon}} \cdot 12 \text{ gallons} =\]
\[\frac{24 \text{ miles}}{\cancel{\text{gallon}}} \cdot 12 \cancel{\text{ gallons}} =\]
\[24 \text{ miles} \cdot 12 =\]
\[288 \text{ miles}\]
3.
A person’s vehicle gets \(30\)
miles per gallon. Their journey on the road is 250 miles. The current
cost per gallon is $3.87. How much will they spend on gas on this
trip?
We can first calculate the number of gallons spent on the trip, then calculate the cost by multiplying $3.87 to the number of gallons.
\[250 \text{ miles} \cdot \frac{1 \text{ gallon}}{30 \text{ miles}}\]
\[250 \cancel{\text{ miles}} \cdot \frac{1 \text{ gallon}}{30 \cancel{\text{ miles}}}\]
\[\frac{250 \text{ gallons}}{30} \approx 8.33 \text{ gallons}\]
Multiply the number of gallons by the cost per gallon.
\[8.33 \text{ gallons} \cdot \frac{\$3.87}{\text{gallon}}\]
\[8.33 \cancel{\text{ gallons}} \cdot \frac{\$3.87}{\cancel{\text{gallon}}}\]
\[8.33 \cdot \$3.87 \approx \$32.24\]
4.
A person suspects that the miles per gallon number given to them
by the car dealership is wrong, so they check the miles per gallon
themselves. The person starts driving on the highway with a full tank of
gas. The person drives \(160\) miles.
They pull over and fill up the tank of gas after some time. They have to
add \(8.5\) gallons to fill up their
tank. What is their miles per gallon for this car?
The miles per gallon is \(\frac{\text{miles}}{\text{gallon}}\), so we will want to divide the number of miles driven by the number of gallons.
\[\frac{160 \text{ miles}}{8.5 \text{ gallons}} \approx 18.82 \frac{\text{miles}}{\text{gallon}}\]
- lots of MPG questions, both calculating distance traveled, gallons spent, etc.
1. A person is going to take a \(240\) mile trip. Their vehicle is said to get 22 miles per gallon. How many gallons should they expect to use for the trip?
2. A car gets 23 miles per gallon. A person did not have their phone GPS turned on and they want to know how far they have traveled. When they gas up, they realized they spent 14 gallons of gas. How far have they traveled?
3. A person’s vehicle gets \(20\) miles per gallon. Their journey on the road is 180 miles. The current cost per gallon is $3.63. How much will they spend on gas on this trip?
4. A person suspects that the miles per gallon number given to them by the car dealership is wrong, so they check the miles per gallon themselves. The person starts driving on the highway with a full tank of gas. The person drives \(220\) miles. They pull over and fill up the tank of gas after some time. They have to add \(9.5\) gallons to fill up their tank. What is their miles per gallon for this car?
1. How would you describe the relationship between miles driven and gallons consumed? Is it a direct relationship, an inverse relationship, an exponential relationship, etc.?
To analyze the relationship, you could consider the following equation for a car that gets \(20\) miles per gallon:
\[\frac{\text{miles driven}}{\text{gallons needed}} = 20\]