Question

Car A gets 25 miles per gallon and costs $13,000. Car B is a hybrid that gets 45 miles per gallon, but costs $25,000. Assume you drive 15,000 miles per year and that gas will cost $4 per gallon for the foreseeable future. How many years will it take for Car B's better fuel economy to outweigh its higher initial cost?

Answer 1

The initial cost of car B is 25,000.

The cost of fuel consumed in n years by car B is 
     $=n\times \frac{15000\:miles}{year}\times \frac{1\:gallon}{45\:miles}\times \frac{4\:dollars}{gallon}$

Equate the initial cost to the cost of fuel
     $25000=n\times \frac{15000\:miles}{year}\times \frac{1\:gallon}{45\:miles}\times \frac{4\:dollars}{gallon}$

     $25000=\frac{4000n}{3}$

     $n=\frac{25000\left(3\right)}{4000}$

     $n=18.75$

It will take 18.75 years for Car B's better fuel economy to outweigh its higher initial cost.