To determine the constant of proportionality and the equation that models the situation, we first need to clarify what the problem describes. If we assume that the situation involves a constant rate of travel, where distance is proportional to time, we can derive the necessary information based on the given responses.
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Constant of Proportionality: This is typically the rate at which distance changes with time. If, for instance, the problem states that something travels at 12.5 miles per minute, the constant of proportionality would be 12.5.
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Equation to Model the Situation: Given the variables for distance (d) and time (t), and assuming that distance equals speed multiplied by time, the relationship can be expressed as follows:
- If the constant speed is 12.5, the relationship is:
\[ d = 12.5t \]
(This means that distance is 12.5 times the time traveled.)
Among the provided responses, the correct equation that models the situation based on the constant of proportionality would be:
d = 12.5t
(d is equal to 12.5 times t)
If the constant speed instead is 0.08 miles per minute, then the modeling equation would change to:
d = 0.08t
(d is equal to 0.08 times t)
Without a specific context, based on the common interpretation of a constant speed, the most appropriate response would generally be \( d = 12.5t \), as it is likely referring to a common unit of measurement for speed in miles per minute.