Question

Consider two people, Blake and Alex, who have similar driving habits. Blake drives an SUV that averages 15 miles/gallon and Alex drives a compact car that averages 35 miles/gallon. If they each upgrade to cars that get an additional five miles per gallon, who saves more gas? What is the ratio of the amount of gas saved by Blake to the amount of gas saved by Alex? For example, if Blake saves x gallons of gas per day and Alex saves y gallons per day, then the ratio to look for here is the number x/y.

Answer 1

Let both of Blake and Alex rides for x miles.

Before getting an additional five miles per gallon, Blake needs (x/15) gallon of gas and Alex needs (x/35) gallon of gas.

After getting an additional five miles per gallon, Blake needs (x/20) gallon of gas and Alex needs (x/40) gallon of gas.

Blake saves = (x/15)-(x/20) = (x/60) gallon of gas

Alex saves = (x/35)-(x/40) = (x/280) gallon of gas

Therefore, Blake saves more gas than Alex.

Ratio of the amount of gas saved by Blake to the amount of gas saved by Alex is = (x/60):(x/280) = 280:60 = 14:3.