Your small remodeling business has two work vehicles. One is a small passenger c

Question

Your small remodeling business has two work vehicles. One is a small passenger car used for job-site visits and for other general business purposes. The other is a heavy truck used to haul equipment. The car gets 25 miles per gallon (mpg). The truck gets 10 mpg. You want to improve gas mileage to save money, and you have enough money to upgrade one vehicle. The upgrade cost will be the same for both vehicles. An upgraded car will get 40 mpg; an upgraded truck will get 12.5 mpg. The cost of gasoline is $3.90 per gallon. Suppose you drive the truck 10,200 miles per year. How many miles would you have to drive the car before upgrading the car would be the better choice? Number of miles

Explanation / Answer

Benefit of upgrading truck = Benefit of upgrading car

Benefit of upgrading truck = Gallons cost without upgrade - Gallons cost with upgrade

= (10200/10-10200/12.5)*3.90 i.e 795.60

Benefit of car should be more then 795.60 to upgrade the car

Increase in mileage of the car due to upgrade = Mileage with upgrade - Milegae without upgrade

= 40-25 i.e 15 miles

Let the mileage driven by car be x

Benefit of upgradingg car = ( X/25-X/40)*3.90

795.60 = 3x/200*3.90

795.60 = 11.70X/200

795.60*200/11.70 = X

159120/11.70 = X

X = 13600 miles

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