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Perform Unit Conversions for Fuel Economy
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Another application of unit conversions is to calculate fuel economy. Fuel economy of vehicles compares the distance the vehicle can go compared to the amount of fuel it uses or the cost of the fuel. In this next video, we use unit conversion to determine the cost of a delivery. The following video will explain how to solve this example:

Unit Conversions for Fuel Economy

Even though our conversion factors look different, the process is the same. Before starting the problem, scan the question to find the conversion rates it gives you, then complete the steps below:

2. Determine what you want to get in the end. (Figure out what the end units should be.)
3. Determine what conversion factor(s) to use. You may sometimes need more than one.
4. Multiply by 1 in the form of the conversion factor that cancels out the unwanted units.

### Practice Problems

1. You are planning to go on a trip with some friends. Your vehicle gets 25 miles per gallon (mpg), and you want to drive from Los Angeles to San Francisco. San Francisco is 382 miles away. The current gas price is $3.75 per gallon. How much will the gas for your trip cost, in US Dollars? Round to the nearest penny (hundredth). 25 mi = 1 gal$3.75 = 1 gal
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Solution
$$\displaystyle \frac{382\:\text{mi}}{1}\times\frac{1\:\text{gal}}{25\:\text{mi}}\times\frac{\3.75}{1\:\text{gal}} = \57.30$$

Written Solution:

Step 1: Start with what you know.

We know that it is 382 miles to San Francisco from Los Angeles.

Step 2: Determine what you want to get in the end (figure out what the end units should be):

We need to find out how much the trip will cost so the units we are looking for are US Dollars.

Step 3: Determine what conversion factor(s) to use:

25 mi = 1 gal

$3.75 = 1 gal Step 4: Multiply by 1 in the form of the conversion factor that cancels out the unwanted units. We are starting with 382 miles and need to find the cost of our trip, so we will multiply 382 miles by the conversion factors that will cancel out miles and gallons and leave us with dollars: $$\displaystyle \frac{382\:\text{mi}}{1}\times\frac{1\:\text{gal}}{25\:\text{mi}}\times\frac{\3.75}{1\:\text{gal}}$$ Note that multiplying by each of the two conversion factors, $$\dfrac{1\:\text{gal}}{25\:\text{mi}}$$ and $$\dfrac{\3.75}{1\:\text{gal}}$$, is the same as multiplying by 1 since the numerator is equal to the denominator in both cases. This is why we can do unit conversions. Then we cancel out miles and gallons: $$\displaystyle \frac{382\:\cancel{{\color{Red} \text{mi}}}}{1}\times\frac{1\:\cancel{{\color{Blue} \text{gal}}}}{25\:\cancel{{\color{Red} \text{mi}}}}\times\frac{\3.75}{1\:\cancel{{\color{Blue} \text{gal}}}}$$ Using the zig-zag method we make the calculations in a zig-zag pattern. Remember, any time we move to the denominator we divide and any time we move to the numerator, we multiply the following: $$382 \div 1 \times 1 \div 25 \times 3.75 \div 1 = 57.3$$ So it will cost$57.30 to drive from Los Angeles to San Francisco.
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2. How much does it cost to drive 23 miles using a truck that takes 10 gallons to go 120 miles, if the current cost of gas is $3.55? Round to the nearest penny (hundredth). 10 gal = 120 mi$3.55 = 1 gal
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Solution
$$\displaystyle \frac{23\:\text{mi}} {1}\times\frac{10\:\text{gal}}{120\:\text{mi}}\times\frac{\3.55}{1\:\text{gal}} = \6.80$$
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3. Pam lives in the mountains far away from any power source. She uses an oil lamp to light her cabin at night. She goes through 3 ounces of oil each night. The current cost of oil is $9 per gallon. How much does it cost Pam to light her cabin each night in US Dollars? Use the following information to find the answer. Round to the nearest penny (hundredth).$9 = 1 gal
3 oz = 1 night
1 gal = 128 oz
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Solution
$$\displaystyle \frac{3\:\text{oz}}{1\:\text{night}}\times\frac{1\:\text{gal}}{128\:\text{oz}}\times\frac{\9}{1\:\text{gal}}= \0.21$$

Written Solution:

Step 1: Start with what you know.

We know that Pam uses 3 ounces of oil per night.

Step 2: Determine what you want to get in the end (figure out what the end units should be):

We need to find out how much the trip will cost so the units we are looking for are US dollars.

Step 3: Determine what conversion factor(s) to use:

$9 = 1 gal 3 oz = 1 night 1 gal = 128 oz Step 4: Multiply by 1 in the form of the conversion factor that cancels out the unwanted units. We are starting with 3 ounces per night. To find the cost, we multiply $$\dfrac{3\:\text{oz}}{1\:\text{night}}$$ by the conversion factors that will enable us to cancel out ounces and gallons and leave us with dollars: $$\displaystyle \frac{3\:\text{oz}}{1\:\text{night}}\times\frac{1\:\text{gal}}{128\:\text{oz}}\times\frac{\9}{1\:\text{gal}}$$ Note that each of the two conversion factors, $$\dfrac{1\:\text{gal}}{128\:\text{oz}}$$ and $$\dfrac{\9}{1\:\text{gal}}$$ are theoretically equal to 1 because anytime you divide something by itself it equals 1. Since the numerator is equivalent to the denominator. Then we cancel out ounces and gallons: $$\displaystyle \frac{3\:\cancel{{\color{Red} \text{oz}}}}{1\:\text{night}}\times\frac{1\:\cancel{{\color{Blue} \text{gal}}}}{128\:\cancel{{\color{Red} \text{oz}}}}\times\frac{\9}{1\:\cancel{{\color{Blue} \text{gal}}}}$$ Using the zig-zag method we make the calculations in a zig-zag pattern. Remember, any time we move to the denominator we divide and any time we move to the numerator, we multiply the following: 3 ÷ 1 night × 1 ÷ 128 ×$9 ÷ 1 = $$\dfrac{0.2109}{1\:\text{night}}$$

So it will cost about \$0.21 per night.
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4. A truck has a fuel efficiency of 9 milliliters per 100 meters. Find the truck’s fuel efficiency in liters per kilometers using the following information.
1 L = 1000 ml
1 km = 1000 m
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Solution
$$\displaystyle \frac{9\:\text{ml}}{100\:\text{m}}\times\frac{1\:\text{L}}{1000\:\text{ml}}\times\frac{1000\:\text{m}}{1\:\text{km}} = \frac{.09\:\text{L}}{1\:\text{km}}$$

(Fuel efficiency is often written as liters per 100 kilometers. If we want to see it this way, we can multiply the numerator and denominator by 100.)

$$\displaystyle \frac{.09\:\text{L}}{1\:\text {km}}\times\frac{100}{100} = \frac {9\:\text{L}}{100\:\text{km}}$$
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5. How much does it cost to drive 45 kilometers using a car that takes 5 liters of petrol (or gasoline) to go 100 kilometers? The current cost of petrol is €1.50.Round to the nearest hundredth.
5 L = 100 km
€1.50 = 1 L
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Solution
$$\displaystyle \frac{45\: {\text{km}}}{1}\times\frac{5\: {\text{L}}}{100\:{\text{km}}}\times\frac{1.50}{1\: {\text{L}}} = 3.38$$
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