Convert 54 miles per gallon into kilometres per litre (km/l).
Use the conversions 5 miles = 8 kilometres and 2 gallons = 9 litres. If your answer is a decimal, give it to 1 d.p.
The correct answer and explanation is:
To convert 54 miles per gallon (mpg) into kilometres per litre (km/l), use the given conversions:
- 5 miles = 8 kilometres
- 2 gallons = 9 litres
Step 1: Convert miles to kilometres
We are given that 5 miles = 8 kilometres. Therefore, to convert 54 miles to kilometres, we can use the ratio: 8 km5 miles=1.6 km/mile\frac{8 \text{ km}}{5 \text{ miles}} = 1.6 \text{ km/mile}
Now, multiply 54 miles by the conversion factor (1.6 km/mile): 54 miles×1.6 km/mile=86.4 km54 \text{ miles} \times 1.6 \text{ km/mile} = 86.4 \text{ km}
Step 2: Convert gallons to litres
We are also given that 2 gallons = 9 litres. To convert from gallons to litres, the ratio is: 9 litres2 gallons=4.5 litres/gallon\frac{9 \text{ litres}}{2 \text{ gallons}} = 4.5 \text{ litres/gallon}
Now, divide 54 miles per gallon by the conversion factor (4.5 litres/gallon): 54 miles1 gallon×8 km5 miles×1 gallon4.5 litres=86.4 km12 litres\frac{54 \text{ miles}}{1 \text{ gallon}} \times \frac{8 \text{ km}}{5 \text{ miles}} \times \frac{1 \text{ gallon}}{4.5 \text{ litres}} = \frac{86.4 \text{ km}}{12 \text{ litres}}
Now, divide the total kilometres by the total litres: 86.4 km12 litres=7.2 km/l\frac{86.4 \text{ km}}{12 \text{ litres}} = 7.2 \text{ km/l}
Final Answer:
The conversion of 54 miles per gallon into kilometres per litre is 7.2 km/l.
This conversion works by applying the correct conversion ratios for miles to kilometres and gallons to litres, ensuring the units are appropriately cancelled out and the result is in the desired units of km/l.