Question

Suppose a car's standard tires are replaced with tires $1.50$ times larger in diameter. What will the car's fuel economy in miles per gallon or $km/L$ appear to be?

• A. $1.50$ times better
• B. $2.25$ times worse
• C. $2.25$ times better
  
• D. $1.50$ times worse
  

Answer 1

The correct option is D $1.50$ times worse


If the driver uses the odometer reading to calculate fuel economy, this reading is a factor of $1.5$ too small because the odometer assumes $1rev=2\pi R$ for a standard tire radius $R,$ whereas the actual distance traveled is $1.5\left(2\pi R\right),$ so the fuel economy in miles per gallon will appear to be lower by a factor of $\mathrm{1.5.}$
Example: If the car travels $15km,$ the odometer will read $10km.$ If the car actually makes $15km/gal,$ the calculation will give $10km/gal.$
Final Answer: $\left(c\right)$