In which situation would you set up a proportion problem?

Setting up a proportion problem is appropriate when comparing quantities to determine how they relate to one another. In the given situation of comparing the time taken by two groups for the same task, a proportion problem allows you to analyze the relative efficiency or performance of each group based on the time they took. By establishing a ratio of the times, you can draw conclusions about which group performed better or how the times relate to a standard or expected value.

Using proportions in this context enables effective comparisons, particularly when you want to express the relationship between the two groups in terms of their performance or responsiveness to the task. This method can be particularly useful in performance evaluations, scheduling, and resource management, where understanding relative efficiencies is crucial for operational decisions.

In contrast, while comparing two fractions may involve similarly related parts, it does not inherently require a proportion setup unless a specific relationship or context is given that necessitates it. Similarly, converting decimals to fractions does not involve a comparison but rather a transformation of the format of representation. Calculating percentages of a whole is another operation that does not directly involve proportional relationships, as it focuses on finding a part related to the whole rather than comparing two distinct quantities.