Difficulty: Hard

Average Score: 46%

Which relationship demonstrates inverse proportionality?

Rationale

The speed at which a runner races one mile and the total time it takes demonstrate inverse proportionality.

In this relationship, as the speed of the runner increases, the total time taken to complete the mile decreases, illustrating the characteristics of inverse proportionality where one variable increases while the other decreases in a consistent manner.

A (Average resting heart rate and score on an intelligence test) YOUR ANSWER

This relationship does not exemplify inverse proportionality as there is no consistent pattern where an increase in one variable reliably leads to a decrease in the other. The average resting heart rate is not necessarily correlated with intelligence scores, and their relationship can vary widely among individuals.

B (The speed at which a runner races one mile and the total time it takes) CORRECT

This choice accurately represents inverse proportionality. When a runner increases their speed, the time taken to complete the mile decreases; hence, the two variables are inversely related. This means that doubling the speed would halve the time taken, clearly demonstrating the inverse nature of their relationship.

C (The volume of gasoline pumped at a gas station and the total cost) YOUR ANSWER

This relationship indicates direct proportionality rather than inverse. As the volume of gasoline pumped increases, the total cost also increases proportionally. This means both variables move in the same direction, which is contrary to the concept of inverse proportionality.

D (The length of a pipe and the total weight of the pipe) YOUR ANSWER

This option also reflects direct proportionality. Generally, as the length of a pipe increases, the weight of the pipe increases as well, assuming uniform material density. Thus, the two variables do not exhibit the characteristics of inverse proportionality.

Conclusion

Inverse proportionality is characterized by a relationship where an increase in one variable results in a decrease in another. The only relationship that meets this criterion in the given options is between the speed at which a runner races one mile and the total time taken. All other choices either do not demonstrate a proportional relationship or exhibit direct proportionality, confirming the unique nature of choice B as the correct answer.

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