A car gets 30 miles to the gallon. If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now. If the fuel tank holds 15 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?
A. 112.5 B. 150 C. 337.5 D. 450 E. 500
(B) After the modification, the vehicle will use less fuel, and will be able to travel 30 miles using just 75% of 1 gallon of fuel, or 0.75 gallons. Therefore, it will travel 30/(0.75), or 40 miles, per gallon of fuel.
Thus, it can travel an additional 10 miles per gallon, and an additional 150 miles per full tank.
The correct answer is choice (B). ----------
Is there another way to understand the logic to this problem? Why can't I take 30 × 15 = 450; 450 × 75% = 337.5 and subtract 450 – 337.5?
Why can't I take 30 × 15 = 450; 450 × 75% = 337.5 and subtract 450 – 337.5?
30 × 15 = 450 miles the car could travel on its full tank before the modification.
450 × 0.75 = 337.5 miles is some irrelevant value. If we want to calculate how far the car can travel on its full tank after the modification we have to divide by 0.75, not to multiply. (Remember, that the car is able to travel MORE after the modification, NOT less.)
So 450 / 0.75 = 600 miles the car can travel on its full tank after the modification.
The increase is 600 – 450 = 150 miles. The correct answer is B.
NOTE, that the key for solving this question is to calculate new consumption rate.
The consumption rate before the modification was 30 miles per gallon = 30 miles / 1 gallon.
If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now.
Therefore the car will travel each 30 miles using just 0.75 of a gallon, not 1 gallon. The consumption rate after the modification is 30 miles / 0.75 gallon = 30/0.75 miles per gallon = 40 miles per gallon.
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