Question

which of the following describes a situation that fits inverse variation?

• the longer you wait, the more interest you earn.
• the faster you drive, the less time it takes to reach your destination.
• the taller a person is, the more they weigh.
• the more hours you work, the more money you earn.

Explanation:

Inverse variation means that as one quantity increases, the other decreases proportionally (their product is constant). Let's analyze each option:

• "The longer you wait, the more interest you earn": Both increase (direct variation), not inverse.
• "The faster you drive, the less time it takes to reach your destination": Speed (\(v\)) and time (\(t\)) are related by \(d = vt\) (distance is constant). So as \(v\) increases, \(t\) decreases, which is inverse variation (since \(v\times t = d\) (constant)).
• "The taller a person is, the more they weigh": Both tend to increase (not a strict inverse, more of a positive correlation), not inverse variation.
• "The more hours you work, the more money you earn": Both increase (direct variation), not inverse.

Answer:

B. The faster you drive, the less time it takes to reach your destination.