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MPG worksheet

Grade 6 · CCSS 6.RP.A.3.b, 6.RP.A.3.d

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- What do you want to do?: Convert a fuel economy figure
- Fuel economy: 30 mpg (US)
Find: Liters per 100 km
Answer
2.
Problem 2.
- What do you want to do?: Calculate from distance and fuel used
- Distance driven: 375 miles
- Fuel used: 10 US gallons
Find: Miles per US gallon
Answer
3.
Problem 3.
- What do you want to do?: Calculate from distance and fuel used
- Distance driven: 260 miles
- Fuel used: 10.4 US gallons
Find: Miles per US gallon
Answer
4.
Problem 4.
- What do you want to do?: Calculate from distance and fuel used
- Distance driven: 370 miles
- Fuel used: 13.5 US gallons
Find: Miles per US gallon
Answer
5.
Problem 5.
- What do you want to do?: Convert a fuel economy figure
- Fuel economy: 39 mpg (US)
Find: Liters per 100 km
Answer
6.
Problem 6.
- What do you want to do?: Convert a fuel economy figure
- Fuel economy: 24 mpg (US)
Find: Liters per 100 km
Answer
7.
Problem 7.
- What do you want to do?: Calculate from distance and fuel used
- Distance driven: 340 miles
- Fuel used: 11.5 US gallons
Find: Miles per US gallon
Answer
8.
Problem 8.
- What do you want to do?: Convert a fuel economy figure
- Fuel economy: 40 mpg (US)
Find: Liters per 100 km
Answer
9.
Problem 9.
- What do you want to do?: Convert a fuel economy figure
- Fuel economy: 26 mpg (US)
Find: Liters per 100 km
Answer
10.
Problem 10.
- What do you want to do?: Convert a fuel economy figure
- Fuel economy: 38 mpg (US)
Find: Liters per 100 km
Answer

Answer key: MPG worksheet

1. Liters per 100 km: 7.84 L/100 km
1. First change to kilometers per liter, the go-between unit: miles become km (× 1.609344) and US gallons become liters (÷ 3.785411784)
  $\frac{30 \times 1.609344}{3.785412}$ $= 12.754311 km/L$
2. Flip it around for liters per 100 km: divide 100 by the km per liter
  $\frac{100}{12.754311}$ $= 7.8405 L/100 km$
3. For miles per imperial gallon, scale km per liter up to an imperial gallon (× 4.54609) and change km to miles (÷ 1.609344)
  $\frac{12.754311 \times 4.54609}{1.609344}$ $= 36.0285 mpg (imp)$
2. Miles per US gallon: 37.5 mpg (US)
1. Change the distance to kilometers, so we can work out the metric figures too (1 mi = 1.609344 km)
  $375 mi \times 1.609344$ $= 603.504 km$
2. Change the fuel to liters for the metric figures (1 US gal = 3.785411784 L)
  $10 US gal \times 3.785412$ $= 37.8541 L$
3. Change the fuel to imperial gallons for the UK mpg figure (÷ 4.54609)
  $\frac{37.8541 L}{4.54609}$ $= 8.3267 imp gal$
4. Miles per US gallon: divide the miles by the US gallons to see how far each gallon took you
  $\frac{375}{10}$ $= 37.5 mpg (US)$
5. Miles per imperial gallon: divide the miles by the imperial gallons
  $\frac{375}{8.3267}$ $= 45.0356 mpg (imp)$
6. Liters per 100 km: divide the liters by the km, then multiply by 100 to see the fuel for every 100 km
  $\frac{37.8541}{603.504} \times 100$ $= 6.2724 L/100 km$
7. Kilometers per liter: divide the km by the liters to see how far each liter took you
  $\frac{603.504}{37.8541}$ $= 15.9429 km/L$
3. Miles per US gallon: 25 mpg (US)
1. Change the distance to kilometers, so we can work out the metric figures too (1 mi = 1.609344 km)
  $260 mi \times 1.609344$ $= 418.4294 km$
2. Change the fuel to liters for the metric figures (1 US gal = 3.785411784 L)
  $10.4 US gal \times 3.785412$ $= 39.3683 L$
3. Change the fuel to imperial gallons for the UK mpg figure (÷ 4.54609)
  $\frac{39.3683 L}{4.54609}$ $= 8.6598 imp gal$
4. Miles per US gallon: divide the miles by the US gallons to see how far each gallon took you
  $\frac{260}{10.4}$ $= 25 mpg (US)$
5. Miles per imperial gallon: divide the miles by the imperial gallons
  $\frac{260}{8.6598}$ $= 30.0237 mpg (imp)$
6. Liters per 100 km: divide the liters by the km, then multiply by 100 to see the fuel for every 100 km
  $\frac{39.3683}{418.4294} \times 100$ $= 9.4086 L/100 km$
7. Kilometers per liter: divide the km by the liters to see how far each liter took you
  $\frac{418.4294}{39.3683}$ $= 10.6286 km/L$
4. Miles per US gallon: 27.41 mpg (US)
1. Change the distance to kilometers, so we can work out the metric figures too (1 mi = 1.609344 km)
  $370 mi \times 1.609344$ $= 595.4573 km$
2. Change the fuel to liters for the metric figures (1 US gal = 3.785411784 L)
  $13.5 US gal \times 3.785412$ $= 51.1031 L$
3. Change the fuel to imperial gallons for the UK mpg figure (÷ 4.54609)
  $\frac{51.1031 L}{4.54609}$ $= 11.2411 imp gal$
4. Miles per US gallon: divide the miles by the US gallons to see how far each gallon took you
  $\frac{370}{13.5}$ $= 27.4074 mpg (US)$
5. Miles per imperial gallon: divide the miles by the imperial gallons
  $\frac{370}{11.2411}$ $= 32.9149 mpg (imp)$
6. Liters per 100 km: divide the liters by the km, then multiply by 100 to see the fuel for every 100 km
  $\frac{51.1031}{595.4573} \times 100$ $= 8.5822 L/100 km$
7. Kilometers per liter: divide the km by the liters to see how far each liter took you
  $\frac{595.4573}{51.1031}$ $= 11.6521 km/L$
5. Liters per 100 km: 6.03 L/100 km
1. First change to kilometers per liter, the go-between unit: miles become km (× 1.609344) and US gallons become liters (÷ 3.785411784)
  $\frac{39 \times 1.609344}{3.785412}$ $= 16.580605 km/L$
2. Flip it around for liters per 100 km: divide 100 by the km per liter
  $\frac{100}{16.580605}$ $= 6.0311 L/100 km$
3. For miles per imperial gallon, scale km per liter up to an imperial gallon (× 4.54609) and change km to miles (÷ 1.609344)
  $\frac{16.580605 \times 4.54609}{1.609344}$ $= 46.837 mpg (imp)$
6. Liters per 100 km: 9.8 L/100 km
1. First change to kilometers per liter, the go-between unit: miles become km (× 1.609344) and US gallons become liters (÷ 3.785411784)
  $\frac{24 \times 1.609344}{3.785412}$ $= 10.203449 km/L$
2. Flip it around for liters per 100 km: divide 100 by the km per liter
  $\frac{100}{10.203449}$ $= 9.8006 L/100 km$
3. For miles per imperial gallon, scale km per liter up to an imperial gallon (× 4.54609) and change km to miles (÷ 1.609344)
  $\frac{10.203449 \times 4.54609}{1.609344}$ $= 28.8228 mpg (imp)$
7. Miles per US gallon: 29.57 mpg (US)
1. Change the distance to kilometers, so we can work out the metric figures too (1 mi = 1.609344 km)
  $340 mi \times 1.609344$ $= 547.177 km$
2. Change the fuel to liters for the metric figures (1 US gal = 3.785411784 L)
  $11.5 US gal \times 3.785412$ $= 43.5322 L$
3. Change the fuel to imperial gallons for the UK mpg figure (÷ 4.54609)
  $\frac{43.5322 L}{4.54609}$ $= 9.5758 imp gal$
4. Miles per US gallon: divide the miles by the US gallons to see how far each gallon took you
  $\frac{340}{11.5}$ $= 29.5652 mpg (US)$
5. Miles per imperial gallon: divide the miles by the imperial gallons
  $\frac{340}{9.5758}$ $= 35.5063 mpg (imp)$
6. Liters per 100 km: divide the liters by the km, then multiply by 100 to see the fuel for every 100 km
  $\frac{43.5322}{547.177} \times 100$ $= 7.9558 L/100 km$
7. Kilometers per liter: divide the km by the liters to see how far each liter took you
  $\frac{547.177}{43.5322}$ $= 12.5695 km/L$
8. Liters per 100 km: 5.88 L/100 km
1. First change to kilometers per liter, the go-between unit: miles become km (× 1.609344) and US gallons become liters (÷ 3.785411784)
  $\frac{40 \times 1.609344}{3.785412}$ $= 17.005748 km/L$
2. Flip it around for liters per 100 km: divide 100 by the km per liter
  $\frac{100}{17.005748}$ $= 5.8804 L/100 km$
3. For miles per imperial gallon, scale km per liter up to an imperial gallon (× 4.54609) and change km to miles (÷ 1.609344)
  $\frac{17.005748 \times 4.54609}{1.609344}$ $= 48.038 mpg (imp)$
9. Liters per 100 km: 9.05 L/100 km
1. First change to kilometers per liter, the go-between unit: miles become km (× 1.609344) and US gallons become liters (÷ 3.785411784)
  $\frac{26 \times 1.609344}{3.785412}$ $= 11.053736 km/L$
2. Flip it around for liters per 100 km: divide 100 by the km per liter
  $\frac{100}{11.053736}$ $= 9.0467 L/100 km$
3. For miles per imperial gallon, scale km per liter up to an imperial gallon (× 4.54609) and change km to miles (÷ 1.609344)
  $\frac{11.053736 \times 4.54609}{1.609344}$ $= 31.2247 mpg (imp)$
10. Liters per 100 km: 6.19 L/100 km
1. First change to kilometers per liter, the go-between unit: miles become km (× 1.609344) and US gallons become liters (÷ 3.785411784)
  $\frac{38 \times 1.609344}{3.785412}$ $= 16.155461 km/L$
2. Flip it around for liters per 100 km: divide 100 by the km per liter
  $\frac{100}{16.155461}$ $= 6.1899 L/100 km$
3. For miles per imperial gallon, scale km per liter up to an imperial gallon (× 4.54609) and change km to miles (÷ 1.609344)
  $\frac{16.155461 \times 4.54609}{1.609344}$ $= 45.6361 mpg (imp)$