To determine the constant of proportionality in Julian's walking scenario, we first need to find the rate at which he walks.
Julian walks 2 miles in 12 hours. To find the rate, we can calculate miles per hour:
\[ \text{Rate} = \frac{2 \text{ miles}}{12 \text{ hours}} = \frac{1}{6} \text{ miles/hour} \]
Now, let's express this in terms of ratios. The context of the question suggests we're looking for a ratio of distance to time. We can represent his distance over time as:
\[ \text{Distance} : \text{Time} = 2 \text{ miles} : 12 \text{ hours} = 1 : 6 \]
If we pair this with the choices provided, we can express the ratio in terms of the distances mentioned in the options. Let's interpret the options:
- (1, 4) - Doesn't match the found ratio.
- (1, 14) - Doesn't match the found ratio.
- (4, 1) - Doesn't match the found ratio.
- (14, 1) - Doesn't match the found ratio.
To relate our finding of \(1 : 6\) to the pairs given, we can convert them into similar terms. For instance, if "1" were part of our distance over time representation:
Since none of the given specified ratios match \(1 : 6\), we can check the reverse.
If we multiply every part of \(1 : 6\) by 2, we reach \(2 : 12\), which adds up to what Julian actually walks.
If we calculate \( \frac{1}{6} \) in terms of the provided options: If we write it as hours per mile, we'd have \(6:1\) (miles per hour). This again doesn't yield similar factors.
Therefore, the best suitable option from the provided choices, where \(1 : 6\) can be expressed, is:
None of the valid options correspond exactly to represent the constant speed ratio correctly.
It seems I cannot clearly pinpoint the correct answer as none matches the initial calculation of his walking speed. Would it make more sense in different context matches? Would you want to clarify further for distance from time?
1 answer