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 kilometers per liter (km/l), we need to use the given conversion factors. These are:
- 5 miles = 8 kilometers
- 2 gallons = 9 liters
Step 1: Convert miles to kilometers
We are given that 5 miles equals 8 kilometers. To convert miles to kilometers, we first divide the number of miles by 5 and then multiply by 8. Therefore: 54 miles×(8 km5 miles)=54×1.6=86.4 kilometers54 \, \text{miles} \times \left(\frac{8 \, \text{km}}{5 \, \text{miles}}\right) = 54 \times 1.6 = 86.4 \, \text{kilometers}
Step 2: Convert gallons to liters
We are given that 2 gallons equals 9 liters. To convert gallons to liters, we divide the number of gallons by 2 and then multiply by 9. Therefore: 1 gallon×(9 liters2 gallons)=1×4.5=4.5 liters1 \, \text{gallon} \times \left(\frac{9 \, \text{liters}}{2 \, \text{gallons}}\right) = 1 \times 4.5 = 4.5 \, \text{liters}
Now, we have 54 miles per gallon converted to 86.4 kilometers per 4.5 liters.
Step 3: Calculate kilometers per liter (km/l)
To find the kilometers per liter, divide the kilometers by the liters: 86.4 km4.5 liters=19.2 km/l\frac{86.4 \, \text{km}}{4.5 \, \text{liters}} = 19.2 \, \text{km/l}
Final Answer:
So, 54 miles per gallon is equivalent to 19.2 kilometers per liter (km/l).
This method uses the provided conversion factors and involves first converting miles to kilometers and gallons to liters, then dividing to find the desired unit of km/l.