Digital SATMath: AlgebraMedium
A car's fuel efficiency, E, in miles per gallon (mpg), varies inversely with its speed, S, in miles per hour (mph), when driving above a certain speed limit. If the car gets 30 mpg at 60 mph, what is its fuel efficiency at 75 mph?
- A24 mpg
- B37.5 mpg
- C20 mpg
- D40 mpg
Show answer & explanationAnswer & explanation
Correct answer: A. 24 mpg
Inverse variation means E = k/S, where k is the constant of proportionality. Using the given values: 30 = k/60, so k = 30 * 60 = 1800. Now, use this constant to find E at 75 mph: E = 1800/75 = 24. So, the fuel efficiency is 24 mpg.
Why the other options are wrong
- B. Incorrect. This would be if it was a direct variation, or 75 mph / 60 mph * 30 mpg.
- C. Incorrect. This would be if the constant k was 1500.
- D. Incorrect. This would be if the constant k was 3000.
Inverse Variation
A relationship between two quantities where their product is constant. As one quantity increases, the other decreases proportionally.
- Can be written as y = k/x or xy = k, where k is the constant of proportionality.
- The graph of an inverse variation is a hyperbola.
- Used to model relationships where an increase in one variable leads to a decrease in another.
Memory trick: Direct goes together, inverse goes apart, constant glue holds them all.